import pandas as pd
import numpy as np
data = {'Name':['Tom', 'Tom', 'Jack', 'Terry'], 'Age':[20, 21, 19, 18]} 
df = pd.DataFrame(data)

nth = ['First', 'Second', 'Third', 'Fourth']

def prefix(d):
    n = len(d)
    if n > 1:
        return d.radd([nth[i] for i in range(n)])
    else:
        return d

df.assign(Name=df.groupby('Name').Name.transform(prefix))

          Name  Age
0     FirstTom   20
1    SecondTom   21
2         Jack   19
3        Terry   18
​