I was just going through lots of Team Tournaments games, just to see how all players were doing and one thing kept jumping out

I kept get lost as to which of the 2 players was on my Team

For all purposes there is nothing (except the Tournament title) that distinguishes a game from any normal game, but unless i hover over that, i do not know who is on which Team.

How about in Team Tournaments & Challenge matches, the Flag of a player is changed for the Fellowship Flag of who they are playing for

It would certainly show who is playing for who, and look quite smart. It actually shows you are playing for a Team, rather than as an individual