Setting flag column depending on whether column contains a given string

You have to remove list, need only string:

df.loc[df['Name'].str.contains('Andy'),'Andy'] = 1

For multiple values chain by |:

df.loc[df['Name'].str.contains('Andy|Andrew'),'Andy'] = 1

pd.Series.str.contains requires for its pat argument a "Character sequence or regular expression", not a list.

Just use Boolean assignment and convert to int. This will set unmatched rows to 0. For example:

# Name includes 'Andy'
df['Andy'] = df['Name'].str.contains('Andy').astype(int)

# Name includes 'Andy' or 'Andrew'
df['Andy'] = df['Name'].str.contains('Andy|Andrew').astype(int)