So I used to assume that the hero that displayed to your allies was the leader of your last Arena match, but now I know that's not the case because I got a request from someone in my Arena and it shows a 5★ VII Consular, whilst his last arena leader was a 4★ VI Barriss.
Perhaps it uses the first character in your ally list (which also seems to be sorted by some kind of average of the three filters; level; power; and rarity.
Would like to find out so if a few people could send me an ally request and post here what my profile hero comes up as I'll post what you appear as and we can try and figure this out.
My ally code is 418-728-123
My allies are currently full, but I'll remove a few if you'd like to keep me as an ally as well for the effort.
I'm level 53 premium player with a couple 6★ heroes and several 5★, 4★, and 3★ heroes I'm upgrading for end game squads. Current PvP rank #1 and team power of 17,600.
I won't need to accept to test this theory out, however can keep this thread updated for anyone participating that I accept whenever we see a change in the ally list displaying our profile hero.