I don’t understand your question. If it’s a multiplayer run for a co-op category on a game, you just type in the username of the second (or third or fourth) player in the designated field on the submission form.
Unless otherwise explicitly stated through a category or rules, all runs are single player only, so if you do a co-op run on a category where it isn’t explicitly meant for co-op, your run is invalid.
If you’re asking how to submit a run on behalf of another person - don’t. That person may not want their run posted and it’s not your place your add it for them. If that person ends up being okay with it being added, contact the mods of the game and let them add the run. Don’t try to submit someone else’s run yourself because it looks suspicious.