The schools announced plans Monday to award the trophy to the winner of the game between the two schools where Tomey used to coach. Hawaii will host San Jose State on Nov. 9 in a Mountain West contest.
Tomey spent 10 years as Hawaii's coach from 1977 to 1986 and helped establish the team as a Division I program. He coached at San Jose State from 2005 to 2009, revitalizing a struggling program.
He spent 14 years at Arizona in between those two stops and had a 183-145-7 career record.
Tomey died May 10 at the age of 80 after battling lung cancer.