diff --git a/dask/array/core.py b/dask/array/core.py
--- a/dask/array/core.py
+++ b/dask/array/core.py
@@ -675,7 +675,7 @@ def map_blocks(
         warnings.warn("The token= keyword to map_blocks has been moved to name=")
         name = token
 
-    name = f"{name or funcname(func)}-{tokenize(func, *args, **kwargs)}"
+    name = f"{name or funcname(func)}-{tokenize(func, dtype, chunks, drop_axis, new_axis, *args, **kwargs)}"
     new_axes = {}
 
     if isinstance(drop_axis, Number):

Looks `map_blocks` tokenization logic has remained unchanged since long, long ago when it was first added in https://github.com/dask/dask/pull/848: https://github.com/dask/dask/blob/a87672e949365075e19cd90b81ddb18f63e3178a/dask/array/core.py#L501

Back at that time, py2 was still a think, so `args` and `kwargs` contained all the arguments to `map_blocks` (including `chunks`).

But these days, `args` and `kwargs` are just the arguments to the function!

@djhoese can you try
```diff
diff --git a/dask/array/core.py b/dask/array/core.py
index 150184f7..4eb03e98 100644
--- a/dask/array/core.py
+++ b/dask/array/core.py
@@ -675,7 +675,7 @@ def map_blocks(
         warnings.warn("The token= keyword to map_blocks has been moved to name=")
         name = token
 
-    name = f"{name or funcname(func)}-{tokenize(func, *args, **kwargs)}"
+    name = f"{name or funcname(func)}-{tokenize(func, dtype, chunks, drop_axis, new_axis, *args, **kwargs)}"
     new_axes = {}
 
     if isinstance(drop_axis, Number):
```
That works for my mini-example above with hacking my installed version of dask. If you need me to try my real world case let me know. Otherwise, this makes sense and seems like a simple fix.
...and I just tested the real world case and that works too!
@djhoese care to open a PR? If not I can get to it eventually.
I will try to find time tonight.
diff --git a/dask/array/tests/test_array_core.py b/dask/array/tests/test_array_core.py
--- a/dask/array/tests/test_array_core.py
+++ b/dask/array/tests/test_array_core.py
@@ -1541,6 +1541,64 @@ def func(dtype, block_info=None):
     assert_eq(x, np.arange(8, dtype=np.float32))
 
 
+def test_map_blocks_unique_name_chunks_dtype():
+    def func(block_info=None):
+        loc = block_info[None]["array-location"]
+        dtype = block_info[None]["dtype"]
+        return np.arange(loc[0][0], loc[0][1], dtype=dtype)
+
+    x = da.map_blocks(func, chunks=((5, 3),), dtype=np.float32)
+    assert x.chunks == ((5, 3),)
+    assert_eq(x, np.arange(8, dtype=np.float32))
+
+    y = da.map_blocks(func, chunks=((2, 2, 1, 3),), dtype=np.float32)
+    assert y.chunks == ((2, 2, 1, 3),)
+    assert_eq(y, np.arange(8, dtype=np.float32))
+    assert x.name != y.name
+
+    z = da.map_blocks(func, chunks=((5, 3),), dtype=np.float64)
+    assert z.chunks == ((5, 3),)
+    assert_eq(z, np.arange(8, dtype=np.float64))
+    assert x.name != z.name
+    assert y.name != z.name
+
+
+def test_map_blocks_unique_name_drop_axis():
+    def func(some_3d, block_info=None):
+        if not block_info:
+            return some_3d
+        dtype = block_info[None]["dtype"]
+        return np.zeros(block_info[None]["shape"], dtype=dtype)
+
+    input_arr = da.zeros((3, 4, 5), chunks=((3,), (4,), (5,)), dtype=np.float32)
+    x = da.map_blocks(func, input_arr, drop_axis=[0], dtype=np.float32)
+    assert x.chunks == ((4,), (5,))
+    assert_eq(x, np.zeros((4, 5), dtype=np.float32))
+
+    y = da.map_blocks(func, input_arr, drop_axis=[2], dtype=np.float32)
+    assert y.chunks == ((3,), (4,))
+    assert_eq(y, np.zeros((3, 4), dtype=np.float32))
+    assert x.name != y.name
+
+
+def test_map_blocks_unique_name_new_axis():
+    def func(some_2d, block_info=None):
+        if not block_info:
+            return some_2d
+        dtype = block_info[None]["dtype"]
+        return np.zeros(block_info[None]["shape"], dtype=dtype)
+
+    input_arr = da.zeros((3, 4), chunks=((3,), (4,)), dtype=np.float32)
+    x = da.map_blocks(func, input_arr, new_axis=[0], dtype=np.float32)
+    assert x.chunks == ((1,), (3,), (4,))
+    assert_eq(x, np.zeros((1, 3, 4), dtype=np.float32))
+
+    y = da.map_blocks(func, input_arr, new_axis=[2], dtype=np.float32)
+    assert y.chunks == ((3,), (4,), (1,))
+    assert_eq(y, np.zeros((3, 4, 1), dtype=np.float32))
+    assert x.name != y.name
+
+
 @pytest.mark.parametrize("func", [lambda x, y: x + y, lambda x, y, block_info: x + y])
 def test_map_blocks_optimize_blockwise(func):
     # Check that map_blocks layers can merge with elementwise layers

Chunks/dtype not considered with map_blocks result name
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**What happened**:

As part of a really long multi-day debug session I've finally figured out the root of my problem. I replaced some old code with a single no-dependency map_blocks function and started to run into some issues when the result was included a larger application that involved rechunking. I've discovered that the main issue is that the `chunks` keyword argument isn't considered in the tokenized name so you can produce two different arrays that result in the same name. This isn't a big problem at first glance as you can do `.compute()` and get the final array you expect, but it is a problem when these arrays start getting used in other tasks that may or may not include chunking. In my use case I ran into cases where if I computed two arrays that were dependent on these similar map_blocks results the scheduler would choose one or the other depending on the order that they were passed to `da.compute(`.

**What you expected to happen**:

Either:

1. Documentation in the `map_blocks` docstring about needing inputs to make the name unique including chunks and dtype. Or how to generate a name "manually" that will include this information as well as the args, kwargs, and function name.
2. Include `chunks` (and maybe other meta information) in the `name` generation for the output.

This would be similar to how you can call `da.zeros` multiple times with the same shape but different chunk size and get arrays with different names.

**Minimal Complete Verifiable Example**:

```python

def test_func(fake_in, block_info=None):
    return np.zeros(block_info[None]['chunk-shape'])

fake_input = 1
res1 = da.map_blocks(test_func, fake_input, chunks=((2,), (3, 3, 2, 1, 1), (2, 2, 2, 1, 1, 1, 1)), meta=np.array((), dtype=np.float64), dtype=np.float64)
res2 = da.map_blocks(test_func, fake_input, chunks=((2,), (6, 2, 2), (6, 4)), meta=np.array((), dtype=np.float64), dtype=np.float64)

res1.name
# 'test_func-7ea2153c7f07c8abd6f3181bc0975958'

res2.name
# 'test_func-7ea2153c7f07c8abd6f3181bc0975958'

## Looks like dtype is the same way

res3 = da.map_blocks(test_func, fake_input, chunks=((2,), (3, 3, 2, 1, 1), (2, 2, 2, 1, 1, 1, 1)), meta=np.array((), dtype=np.float32), dtype=np.float32)

res3.name
# 'test_func-7ea2153c7f07c8abd6f3181bc0975958'

```

**Anything else we need to know?**:

This may be related to https://github.com/dask/dask/issues/6649.

**Environment**:

- Dask version: 2021.11.2 (but seen on multiple)
- Python version: 3.9
- Operating System: PopOS
- Install method (conda, pip, source): conda/conda-forge


dask/array/tests/test_array_core.py::test_map_blocks_unique_name_drop_axis dask/array/tests/test_array_core.py::test_map_blocks_unique_name_new_axis dask/array/tests/test_array_core.py::test_map_blocks_unique_name_chunks_dtype
dask/array/tests/test_array_core.py::test_normalize_chunks_nan dask/array/tests/test_array_core.py::test_stack_scalars dask/array/tests/test_array_core.py::test_astype dask/array/tests/test_array_core.py::test_meta[dtype1] dask/array/tests/test_array_core.py::test_vindex_basic dask/array/tests/test_array_core.py::test_from_array_with_missing_chunks dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index11-value11] dask/array/tests/test_array_core.py::test_reshape[original_shape15-new_shape15-2] dask/array/tests/test_array_core.py::test_from_array_scalar[int32] dask/array/tests/test_array_core.py::test_elemwise_uneven_chunks dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape3-v_shape3] dask/array/tests/test_array_core.py::test_to_hdf5 dask/array/tests/test_array_core.py::test_matmul dask/array/tests/test_array_core.py::test_map_blocks_block_info_with_new_axis dask/array/tests/test_array_core.py::test_to_delayed_optimize_graph dask/array/tests/test_array_core.py::test_concatenate_axes dask/array/tests/test_array_core.py::test_broadcast_to_scalar dask/array/tests/test_array_core.py::test_reshape[original_shape31-new_shape31-chunks31] dask/array/tests/test_array_core.py::test_Array_computation dask/array/tests/test_array_core.py::test_store_deterministic_keys[True-False] dask/array/tests/test_array_core.py::test_compute_chunk_sizes_warning_fixes_to_zarr dask/array/tests/test_array_core.py::test_normalize_chunks_tuples_of_tuples dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape4-v_shape4] dask/array/tests/test_array_core.py::test_no_chunks_yes_chunks dask/array/tests/test_array_core.py::test_map_blocks_block_info dask/array/tests/test_array_core.py::test_asanyarray dask/array/tests/test_array_core.py::test_broadcast_to_chunks dask/array/tests/test_array_core.py::test_block_simple_column_wise dask/array/tests/test_array_core.py::test_vindex_negative 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dask/array/tests/test_array_core.py::test_from_array_list[x0] dask/array/tests/test_array_core.py::test_store_deterministic_keys[False-True] dask/array/tests/test_array_core.py::test_from_array_meta dask/array/tests/test_array_core.py::test_from_array_scalar[clongdouble] dask/array/tests/test_array_core.py::test_block_nested dask/array/tests/test_array_core.py::test_reshape[original_shape8-new_shape8-4] dask/array/tests/test_array_core.py::test_blockwise_zero_shape dask/array/tests/test_array_core.py::test_broadcast_arrays dask/array/tests/test_array_core.py::test_reshape[original_shape25-new_shape25-6] dask/array/tests/test_array_core.py::test_Array_numpy_gufunc_call__array_ufunc__02 dask/array/tests/test_array_core.py::test_from_zarr_name dask/array/tests/test_array_core.py::test_reshape[original_shape14-new_shape14-2] dask/array/tests/test_array_core.py::test_blockwise_1_in_shape_III dask/array/tests/test_array_core.py::test_reshape[original_shape5-new_shape5-chunks5] 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dask/array/tests/test_array_core.py::test_concatenate_rechunk dask/array/tests/test_array_core.py::test_from_array_scalar[float] dask/array/tests/test_array_core.py::test_concatenate_zero_size dask/array/tests/test_array_core.py::test_top_with_kwargs dask/array/tests/test_array_core.py::test_zarr_pass_mapper dask/array/tests/test_array_core.py::test_dont_dealias_outputs dask/array/tests/test_array_core.py::test_view_fortran dask/array/tests/test_array_core.py::test_stack dask/array/tests/test_array_core.py::test_top dask/array/tests/test_array_core.py::test_normalize_chunks_auto_1d[24-5-expected3] dask/array/tests/test_array_core.py::test_point_slicing dask/array/tests/test_array_core.py::test_setitem_2d dask/array/tests/test_array_core.py::test_store_method_return dask/array/tests/test_array_core.py::test_from_array_tasks_always_call_getter[x2-1] dask/array/tests/test_array_core.py::test_pandas_from_dask_array dask/array/tests/test_array_core.py::test_broadcast_arrays_uneven_chunks 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