BUG: set Index parameter to False in Index.to_series doesn't work as expected
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
# Your code here
In [1]: import pandas as pd

In [2]: idx = pd.Index(['Ant', 'Bear', 'Cow'], name='animal')

In [3]: idx.to_frame(index=False)
Out[3]: 
  animal
0    Ant
1   Bear
2    Cow

In [4]: idx.to_series(index=False)
```

#### Traceback

<details>

```python
TypeError                                 Traceback (most recent call last)
<ipython-input-4-bc071128e429> in <module>
----> 1 idx.to_series(index=False)

pandas\core\indexes\base.py in to_series(self, index, name)
   1053             name = self.name
   1054
-> 1055         return Series(self.values.copy(), index=index, name=name)
   1056
   1057     def to_frame(self, index: bool = True, name=None):

pandas\core\series.py in __init__(self, data, index, dtype, name, copy, fastpath)
    239
    240             if index is not None:
--> 241                 index = ensure_index(index)
    242
    243             if data is None:

pandas\core\indexes\base.py in ensure_index(index_like, copy)
   5557             index_like = copy_func(index_like)
   5558
-> 5559     return Index(index_like)
   5560
   5561

pandas\core\indexes\base.py in __new__(cls, data, dtype, copy, name, tupleize_cols, **kwargs)
    403
    404         elif data is None or is_scalar(data):
--> 405             raise cls._scalar_data_error(data)
    406         elif hasattr(data, "__array__"):
    407             return Index(np.asarray(data), dtype=dtype, copy=copy, name=name, **kwargs)

TypeError: Index(...) must be called with a collection of some kind, False was passed
```

</details>

#### Problem description

You can't specify index parameter to False in `pandas.Index.to_series` to achieve the same index result with `pandas.Index.to_frame`. It would be more intuitive if we could also specify index to False in `pandas.Index.to_series` and get default index, to match its counterpart.

#### Expected Output
```python
In [4]: idx.to_series(index=False)
Out[4]: 
0     Ant
1    Bear
2     Cow
Name: animal, dtype: object
```
#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : 6ea1855489f5b1cc885ba1163451ccb717686ceb
python           : 3.8.2.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.16299
machine          : AMD64
processor        : Intel64 Family 6 Model 61 Stepping 4, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : English_United States.1252

pandas           : 1.1.0.dev0+1650.g6ea185548
numpy            : 1.17.5
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.1.1
setuptools       : 46.4.0.post20200518
Cython           : 0.29.19
pytest           : 5.4.2
hypothesis       : 5.15.1
sphinx           : 3.0.3
blosc            : None
feather          : None
xlsxwriter       : 1.2.8
lxml.etree       : 4.5.1
html5lib         : 1.0.1
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.14.0
pandas_datareader: None
bs4              : 4.9.1
bottleneck       : 1.3.2
fastparquet      : 0.4.0
gcsfs            : None
matplotlib       : 3.2.1
numexpr          : 2.7.1
odfpy            : None
openpyxl         : 3.0.3
pandas_gbq       : None
pyarrow          : 0.17.1
pytables         : None
pyxlsb           : None
s3fs             : 0.4.2
scipy            : 1.3.2
sqlalchemy       : 1.3.17
tables           : 3.6.1
tabulate         : 0.8.7
xarray           : 0.15.1
xlrd             : 1.2.0
xlwt             : 1.3.0
numba            : 0.49.1
</details>

If possible, I would really love to work on this issue.