I have a dataframe that looks like this:

How can I change the Unnamed: 0 and the blank header of columns so it would look like this:

>Solution :
You want to change both the names of index and columns axis.
You can do it like this:
df.index.name = 'BBID'
df.columns.name = 'VALUE_DATE'
or with a chained method like this:
df = df.rename_axis('VALUE_DATE').rename_axis('BBID', axis=1)