It’s a nice touch in Destiny and GTA that you can have your clan-name on your emblem. After dusting off a tough raid it feels extra rewarding and ‘in-groupy’ to see your clan-name / shared-identity acknowledged in the game.
Conversely, playing as the monster, it would be more satisfying to wipe out a team with a team name.
I’m sure there are legit psycho-anthropological / Activisionological hypno-reasons why this might make a game more compelling.
In terms of 4 v 1, I think it strengthens the idea of a contest when both opponents can each go by a single name.
I can also see how it might be a little jarring thematically to the highly individualistic frontiersman vibe of the game.