Update Pandas DataFrame for each string in a list

Not really sure what your expected output is. Do you mean you want one column per team? You currently keep creating columns but with the same name so always only the one in the last iteration will be kept, the rest overwritten. Or do you want multiple DataFrames?

If you want multiple columns, one per team:

import pandas as pd

df = pd.DataFrame({'game': [1, 2, 3, 4], 'home_team': ['a', 'b', 'c', 'a']})
>    game home_team
  0     1         a
  1     2         b
  2     3         c
  3     4         a

First collect unique teams as you did:

home_list = list(df.home_team.unique())

Create a column for each team:

for team in home_list:
    df[f'home_or_away_{team}'] = [int(ht==team) for ht in df['home_team']]

Which results in:

>   game home_team  home_or_away_a  home_or_away_b  home_or_away_c
 0     1         a               1               0               0
 1     2         b               0               1               0
 2     3         c               0               0               1
 3     4         a               1               0               0

You're over complicating it. Don't need to iterate with numpy .where(). Just use the np.where() on the 2 columns (not with a separate function).

Basically says "where home_team equals team_name, put a 1, else put 0"

import pandas as pd
import numpy as np

df = pd.DataFrame([['Chicago Bears','Chicago Bears', 'Green Bay Packers'],
                   ['Chicago Bears','Green Bay Packers', 'Chicago Bears'],
                   ['Detriot Lions','Detriot Lions', 'Los Angeles Chargers'],
                   ['New England Patriots','New York Jets', 'New England Patriots'],
                   ['Houston Texans','Los Angeles Rams', 'Houston Texans']], 
                  columns = ['team_name','home_team','away_team'])


df['home_or_away'] = np.where(df['home_team'] == df['team_name'], 1, 0)

Output:

print(df)
              team_name          home_team             away_team  home_or_away
0         Chicago Bears      Chicago Bears     Green Bay Packers             1
1         Chicago Bears  Green Bay Packers         Chicago Bears             0
2         Detriot Lions      Detriot Lions  Los Angeles Chargers             1
3  New England Patriots      New York Jets  New England Patriots             0
4        Houston Texans   Los Angeles Rams        Houston Texans             0