There's a team entered in the Tour of California called Team Type 1 which is the type of diabetes the founders have.

I can think of many other "teams" that aren't named after their sponsors. As a matter of fact, I believe back in the day, USCF teams' official names could not be a sponsor. I think they threw that out when people were referring to the sponsors so much that few people knew the official team name. Plus, they were getting creative to make the names refer to their sponsors anyway.