The country band Sawyer Brown fits the bill, too.
On the opposite side of the fence, when I first heard the name “Ben Folds Five”, I figured it was a “Jimmy Eat World” kinda thing, and that there must be a backstory about a guy named Ben rolling five joints at once or something.
Alan Parsons Project
Tommy Tutone? Am I the only one who remembers 867-5309?
I’m pretty sure Alan Parsons is the Alan Parsons of the Alan Parsons Project 
Who sired the bastard child Blodwyn Pig.
Elizabeth – Lillian Roxon wrote about them in The Rock Encyclopedia, but I can’t find anything online. They were an all-male group that released a couple of singles. It also looks like a Canadian indie group uses the name.
Flash and the Pan – no one named “Flash” in the group.
OTOH, Taj Mahal sounds like the name of a group, but he’s a real person.
Marilyn Manson
But he’s not the lead singer. He’s the producer.
My mistake then. Wiki has them both listed as vocals and I didn’t know enough to say there was a big difference.
That’ll learn me 
Daniel Amos
For that matter, J. Geils was never the lead singer of the J. Geils Band.
Marshall Tucker
Son Volt
It’s an easy mistake to make. Two of the Project’s biggest hits (“Time” and “Eye in the Sky”) were sung by Eric Woolfson, whom many people (in my experience) assume to be Parsons.
This is a band now?
Such as Jesus and Mary Chain.
Given your username, I’m surprised you didn’t suggest Chagall Guevara.
Led Zeppelin? That would let in Iron Butterfly and Concrete Blonde. 
Anyway, how about:
The James Gang
Sniff ‘n’ the Tears
Big Brother and the Holding Company
Duran Duran
General Public
Judas Priest
The Freddie Jones Band
After Woolfson’s departure, Alan Parsons went on to release more albums credited to “Alan Parsons” (as opposed to “The Alan Parsons Project”), but he still didn’t sing lead on them.