Benmont Tench is a keyboardist and he was still with Petty when you made your post..
Draft Barron Trump

Jarmusch is a real music fan, and there are many references to music people in the film:
One of the wanted posters Blake reads about himself says that one of the people he is accused of killing is Benmont Tench. As you said, that's the name of a guy in the Tom Petty and the Heartbreakers band. He has also done session work for many other prominent music artists (including Stevie Nicks, Bob Dylan, Johnny Cash, Roy Orbison, Jackson Browne, John Prine, Ringo Starr, Linda Ronstadt, Alanis Morissette, Elvis Costello, Eurythmics, Brian Setzer, Fiona Apple, U2, the dBs, and X).
The wanted poster also says Blake killed L Hazelwood (Lee Hazelwood was a prominent singer/songwriter and music artist from the 1950s and 1960s, known for working with Duane Eddy and Nancy Sinatra.)
The wanted poster also says Blake killed Big George Drakoulious (George Drakoulias was a musician, and a music producer for The Black Crowes.)
The wanted poster also says Blake killed M Throneberry (Marv Throneberry was a major league baseball player. Granted, this is not a reference to a music person. But Throneberry seems like such an unusual name that it makes me think that there's a reasonable chance the wanted poster is referencing this baseball player.)
And Jarmusch had Neil Young doing the score and Iggy Pop acting in the movie.
And the cowboy seen receiving oral sex from a prostitute in an alleyway near the beginning of the film is none other than Gibby Haynes, the lead singer of the Butthole Surfers.

He was the character played by Jared Harris (in the scene with Iggy Pop and Billy Bob Thorton)