From here what I understand DataFrames are:
DataFrame is a 2-dimensional labeled data structure with columns of potentially different types. You can think of it like a spreadsheet or SQL table, or a dict of Series objects.
And Series are:
Series is a one-dimensional labeled array capable of holding any data type (integers, strings, floating point numbers, Python objects, etc.).
Series have a name
attribute which can be accessed like so:
In [27]: s = pd.Series(np.random.randn(5), name='something')
In [28]: s
Out[28]:
0 0.541
1 -1.175
2 0.129
3 0.043
4 -0.429
Name: something, dtype: float64
In [29]: s.name
Out[29]: 'something'
EDIT: Based on OP's comments, I think OP was looking for something like:
>>> df = pd.DataFrame(...)
>>> df.name = 'df' # making a custom attribute that DataFrame doesn't intrinsically have
>>> print(df.name)
'df'