$a  $b  $c  $d  $e
0   1   2   3   4   5

import pandas as pd
 
df = pd.DataFrame({'$a': [1], '$b': [2], '$c': [3], '$d': [4], '$e': [5]})

df.columns = ['a', 'b', 'c', 'd', 'e']

df.columns = df.columns.str.strip('$')

df.columns = df.columns.map(lambda x: x[1:])

df.rename(columns=('$a': 'a', '$b': 'b', '$c': 'c', '$d': 'd', '$e': 'e'}, inplace=True) 

df.rename(columns=lambda x:x.replace('$',''), inplace=True)

import pandas as pd
d={'one':{'a':1,'b':2,'c':3,'d':4},'two':{'a':5,'b':6,'c':7,'d':8},'three':{'a':9,'b':10,'c':11,'d':12}}
df=pd.DataFrame(d)
print(df)
1
2
3
4

df.rename(columns={'two':'twotwo'},inplace=True)
print(df)
1
2

df.rename(index={'a':'aa','b':'bb'},inplace=True)
print(df)
1
2

df.columns=['onon','twtw','thth']
print(df)
1
2