DataFrame.copy(deep=True) is not a deep copy of the index
#### Code Sample, a copy-pastable example if possible

```python
df1 = pd.DataFrame(index=['a', 'b'], columns=['foo', 'muu'])
df1.index.name = "foo"
print(df1)

# create deep copy of df1 and change a value in the index
df2 = df1.copy(deep=True)
df2.index.name = "bar"
df2.index.values[0] = 'c'  # changes both df1 and df2

print(df1)
print(df2)

```
#### Problem description

DataFrame.copy(deep=True) is not a deep copy of the index.

In  

https://github.com/pandas-dev/pandas/blob/a00154dcfe5057cb3fd86653172e74b6893e337d/pandas/core/indexes/base.py#L787

maybe deep should be set to True?

#### Expected Output

```
     foo  muu
foo          
a    NaN  NaN
b    NaN  NaN
     foo  muu
foo          
c    NaN  NaN
b    NaN  NaN
     foo  muu
bar          
c    NaN  NaN
b    NaN  NaN
```
#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit: None
python: 3.6.3.final.0
python-bits: 64
OS: Linux
OS-release: 4.4.0-53-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

pandas: 0.21.0
pytest: 3.2.1
pip: 9.0.1
setuptools: 36.5.0.post20170921
Cython: 0.26.1
numpy: 1.13.1
scipy: 0.19.1
pyarrow: 0.8.0
xarray: 0.9.6
IPython: 6.1.0
sphinx: 1.6.3
patsy: 0.4.1
dateutil: 2.6.1
pytz: 2017.2
blosc: None
bottleneck: 1.2.1
tables: 3.4.2
numexpr: 2.6.2
feather: None
matplotlib: 2.0.2
openpyxl: 2.4.8
xlrd: 1.1.0
xlwt: 1.3.0
xlsxwriter: 0.9.8
lxml: 3.8.0
bs4: 4.6.0
html5lib: 0.999999999
sqlalchemy: 1.1.13
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: 0.5.0

</details>
