List    Numb    Name
1       1       one
1       2       two
2       3       three
4       4       four
3       5       five

List    Numb    Name
one     1       one
one     2       two
two     3       three
four    4       four
three   5       five

df['List'] = df['List'].map(df.set_index('Numb')['Name'])


    List    Numb    Name
0   one     1   one
1   one     2   two
2   two     3   three
3   four    4   four
4   three   5   five

import pandas as pd

df = pd.DataFrame({'List': [1, 1, 2, 4, 3], 'Numb': [1, 2, 3, 4, 5], 'Name': ['one', 'two', 'three', 'four', 'five']})

d = dict(zip(df['Numb'], df['Name']))
df = df.replace({'List': d})

df.rename(columns={"List": "List_numb"}).join(df.set_index("Numb")["Name"].to_frame("List"), on="List_numb")[["List", "Numb", "Name"]]

df['List'] = df.set_index('Numb')['Name'].reindex(df['List']).values

print(df)

    List  Numb   Name
0    one     1    one
1    one     2    two
2    two     3  three
3   four     4   four
4  three     5   five

import pandas as pd

df = pd.DataFrame({
        'List': [1,1,2,4,3],
        'Numb': [1,2,3,4,5],
        'Name':['one','two','three','four','five']
        })

dfnew = pd.merge(df, df, how='inner', left_on=['List'], right_on=['Numb'])
dfnew = dfnew.rename({'List_x': 'List', 'Numb_x': 'Numb', 'Name_y': 'Name'}, axis='columns')
dfnew = dfnew[['List','Numb','Name']]
dfnew['List'] = dfnew['Name']

print (dfnew)
#    List  Numb   Name
#0    one     1    one
#1    one     2    one
#2    two     3    two
#3   four     4   four
#4  three     5  three

df['List'] = df['List'].map(pd.Series(df['Name'].values, df['Numb']))

>>> df
    List  Numb        Name
0      1     0       one_0
1      1     1       two_1
2      2     2     three_2
3      4     3      four_3
4      3     4      five_4
..   ...   ...         ...
0      1  4995    one_4995
1      1  4996    two_4996
2      2  4997  three_4997
3      4  4998   four_4998
4      3  4999   five_4999

[5000 rows x 3 columns]

# Timings (i5-6200U CPU @ 2.30GHz, but only relative times are interesting)
>>> %timeit df.set_index('Numb')['Name'].reindex(df['List']).values # jpp
1.24 ms ± 81.5 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
>>> %timeit df['List'].map(df.set_index('Numb')['Name']) # Vaishali
1.01 ms ± 3.61 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
>>> %timeit df['List'].map(pd.Series(df['Name'].values, df['Numb'])) # timgeb
427 µs ± 4.33 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)