Set column name for apply result over groupby

You could convert your series to a dataframe using reset_index() and provide name='yout_col_name' -- The name of the column corresponding to the Series values

(df_grp.apply(lambda x: x['C'].sum() * x['D'].mean() / x['E'].max())
      .reset_index(name='your_col_name'))

   A  B  your_col_name
0  X  N   5.583333
1  Y  M   2.975000
2  Y  N   3.845455

Have the lambda function return a new Series:

df_grp.apply(lambda x: pd.Series({'new_name':
                    x['C'].sum() * x['D'].mean() / x['E'].max()}))
# or df_grp.apply(lambda x: x['C'].sum() * x['D'].mean() / x['E'].max()).to_frame('new_name')

     new_name
A B          
X N  5.583333
Y M  2.975000
  N  3.845455