We just say "straight man". There isn't really an equivalent verb.
Classic American straight men: Dean Martin (with Jerry Lewis), Bing Crosby (with Bob Hope), Bud Abbott (with Lou Costello), Oliver Hardy (with Stan Laurel), Dick Smothers (with his brother Tom Smothers), um…
That style of comedy fell out of fashion here a while ago. It was a holdover from vaudeville, but in the age of television, individual stars won out. For example, Jackie Gleason and Art Carney started as a team on "The Honeymooners", but over time, Gleason became the breakout star.