The Mosquitos were played by a real-life group called the Wellingtons. They also played the theme songs for Gilligan’s Island and Davy Crockett.
Tess Turbo and the Blackheads.
Moloch, a KISS-like metal singer, played by Donny Most on an episode of CHiPs
La Llorona - Hopey and Terry’s band from Love and Rockets
The Soggy Bottom Boys (O Brother)
I’d love to have a Whotles shirt.
Max Rebo Band, from* Return of the Jedi* - "The group are classified as Jizz-wailers, which, according to the Star Wars Encyclopedia, refers to a “musician who plays a fast, contemporary, and upbeat style of music.” - from Wikipedia
A fictional band whose T-shirt I would not like to own is Blues Hammer from Ghost World.
Ape Sex - also from Love & Rockets
The Bulldaggers - Savage Henry
btw, first time I saw the thread title, I thought it was Fictional performers you would like to see in a wet t-shirt.
You can get a Honey Bees t-shirt.
I want one.
That’s easy – Jessica Rabbit
Follow-up is Holly Would
The Beets (Doug)
I read somewhere that one of the Monty Python guys was driving down the road, listening to a Top 40 station some time in the mid 1990s, and when the announcer said that the previous song was by Toad the Wet Sprocket, he nearly drove off the road.
When the Spinal Tap movie came out, they did indeed have t-shirts with the logo on the front and tour dates listed on the back, with the word “CANCELLED” overlaid.
I wouldn’t mind having a Geronimo Jackson t-shirt either; that band was part of the “Lost” series.
Josie And The Pussycats!
Awesome! I just ordered the one in the first link. 
No matter where you go…there you are!
The Oneders (That Thing You Do!)
Another vote for The Honeybees, as well as The Mosquitos (especially if it had the band member’s names on it (Bingo, Bango, Bongo, and Irving).
I used to own several of the T-shirts that Sheldon wears on Big Bang Theory. Though I had actually purchased them before the show was even a thing.
So apparently I had T-shirts that a fictional character would like to own.
Capitalist Emulsification - It’s the punk band that one of the teachers in Those Who Can’t used to be in. It’s actually available for sale but I don’t want it $25 worth.
Sonic Death Monkey and Kathleen Turner Overdrive - Two of the band names for Jack Black’s band in High Fidelity.
Dr Teeth and the Electric Mayhem Band - It’s from the Muppet Show and has mayhem in the name. “EAT DRUMMMMMSSS!!!” - Animal
The Gories–a proto-Goth band featured on an episode of “Gidget” (they almost broke up Gidget and Larue!).
Tiny Cowboy from “Phineas and Ferb”, voiced by no other than Davy Jones and Peter Noone.
And I’m seriously thinking of getting this shirt–Sev’ral Timez, a boy band from a “Gravity Falls” episode.
The Stray Cats.
No, not Brian Setzer’s band, but the fictional group from “That’ll Be The Day”, featuring Keith Moon, Dave Edmunds and David Essex.