There are numerous ways to add friends in Rumble League. Once you’ve played a match, you’ll see in the Social menu a “recommended” section on the right. These are players you’ve played with recently that you can add.
Another option is to search for your friend’s ‘Rumble tag’. You can do this by typing the tag in the search bar of the Social menu.
Lastly, you can add a party mate to be your friend, simply tap on their name and tap ‘add friend’.