Groupby names replace values with there max value in all columns pandas

Try using pd.wide_to_long to melt that dataframe into a long form, then use groupby with transform to find the max value. Map that max value to 'name' and reshape back to four column (wide) dataframe:

df_long = pd.wide_to_long(df.reset_index(), ['name','val'], 'index', j='num',sep='',suffix='\d+')
mapper= df_long.groupby('name')['val'].max()
df_long['val'] = df_long['name'].map(mapper)
df_new = df_long.unstack()
df_new.columns = [f'{i}{j}' for i,j in df_new.columns]
df_new

Output:

      name1 name2  val1  val2
index                        
0       AAA   BBB    31    22
1       BBB   AAA    22    31
2       BBB   CCC    22    15
3       CCC   AAA    15    31
4       DDD   EEE    25    35

Borrow Scott's setting up

df_long = pd.wide_to_long(df.reset_index(), ['name','val'], 'index', j='num',sep='',suffix='\d+')
d = df_long.groupby('name')['val'].max()

df.loc[:,df.columns.str.startswith('val')]=df.loc[:,df.columns.str.startswith('name')].replace(d).values
df
Out[196]: 
  name1  val1 name2  val2
0   AAA    31   BBB    22
1   BBB    22   AAA    31
2   BBB    22   CCC    15
3   CCC    15   AAA    31
4   DDD    25   EEE    35

You can use lreshape (undocumented and ambiguous as to whether it's tested or will continue to remain) to get the long DataFrame, then map each pair of columns using the max.

names = df.columns[df.columns.str.startswith('name')]
vals = df.columns[df.columns.str.startswith('val')]

s = (pd.lreshape(df, groups={'name': names, 'val': vals})
       .groupby('name')['val'].max())

for n in names:
    df[n.replace('name', 'val')] = df[n].map(s)

---

  name1  val1 name2  val2
0   AAA    31   BBB    22
1   BBB    22   AAA    31
2   BBB    22   CCC    15
3   CCC    15   AAA    31
4   DDD    25   EEE    35