alt Hacker NewsOverwatch (1) had something like that. Not sure if Overwatch (2) still has it, or how it functions now.
In higher ELO, people would target good players with "avoid player"^1, effectively soft-banning those people from match making because the pool was small enough. They would still get put in matches eventually but their queues would blow out a lot.
From memory it did not have an explicit "match me with this person" button, but you could thumbs up players in the post-match podium as well as endorse them which may have soft-factored into matching you with them again.
\1 I think it was called this. It was a general "bad attitude" marker, not a "bad team mate" or "bad opponent" marker.
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Overwatch (1 and 2) had/have an avoid system, but it only avoids as teammate. Overwatch 1 use to at the very beginning have a system to avoid a player as a whole and they wouldn't be matched in your game at all, but that was remove really early on, as it is easily abusable against good player (I don't want them on the enemy team, they are too good so just get rid of them entirely) and there was a report system anyway for other kinda bad stuff.
Then there is just the endorsement system, which is just a level from 1-5 and you can endorse people you liked playing with. It doesn't really do much in matchmaking but you can't do certain things if you are below a certain level (I forgot what all it was but you can't make (public?) custom games if you are too low and I think text and voice chat could also get disabled if you are too low).
Overwatch 2 has a simplified endorsement system. It's just an optional thumbs up instead of endorsement for 1 of 3 reasons (roughly something like sportsmanship, good teammate, or good leader).
The avoid system is now more flexible. You have 3 pin slots for people you never really want to see on your team again, plus 12(?) regular avoid slots to avoid people for a week at a time like usual. In situations where too many avoid conflicts occur and the matchmaker struggles to create a match (e.g. high ELO), it will start to ignore people's avoid slots in order of (last regular avoid > first regular avoid > pin slots), i think.