Dylan Jackson, 20, of no fixed address, is being sought after Herman Simpson, known as Louis, was killed at a bedsit in Compton Road, Wolverhampton, on Monday night.
Members of the public should not approach Mr Jackson, but should call 101, West Midlands Police said.
The force also asked Mr Jackson to contact them himself.
Det Insp Warren Hines said: "Our investigation is moving swiftly and we now have a suspect who we urgently need to trace.
"I would appeal to Dylan directly to contact me as soon as possible but equally, I would ask anyone who knows of his whereabouts, to ring 101.
"Our thoughts remain with Mr Simpson's family."
Detectives have named a man wanted "urgently" in connection with a fatal stabbing.