Figured it out trying to write this, but if anyone have the same issue, the key is in the group.index, and using .loc not .iloc

for name, group in group_by_class:
    mask = group["child"].notna()
    parent_name = group[mask]["name"].values[0]
    print(group.index)
    df.loc[group.index, 'parents_in_group'] = parent_name
    

    
df