Welsh singer (now turned actress I believe) Aimee Anne Duffy recorded as just Duffy.
As a musician she has worked with former Suede guitarist Bernard Butler who himself, after leaving Suede, formed a duo with David McAlmont called McAlmont & Butler.
TCMF-2L
Another one occurring to me is Coverdale/Page.
This thread also provides some pretty hilarious examples of short lived vanity projects.
Lots more duos: Ashford & Simpson, Brooks & Dunn, Fripp & Eno, Peters & Lee.
Crosby, Stills & Nash (before they added Young)
Dawes is a surname, but not of anybody in the band. It’s just the name of the band.
My surprising contribution to the thread: Kongos. Four brothers, that’s their actual last name.
Dang, I forgot about them!
Now you’ve done it. Some researcher 1,000 years from now will see your post and think Dr. Joyce Brothers was in the Allman Brothers Band. 
Hoobastank.
Hoobastank always sound made up to me. I had not realized it was the name of one of the members.
I forgot about Tremonti.
Yes had many members over the years and at one point they split into two factions, one of which used the name Anderson Bruford Wakeman Howe.
J. Giels
And stetching it… The Ramones
It’s not. It’s a nonsense word that they’ve given multiple explanations for. But it doesn’t even resemble the names of any of the founding members (Doug Robb, Dan Estrin, Chris Hesse, and Markku Lappalainen).
Wilson-Phillips
Duffy and Morrisey, depending on whether you consider them bands or solo acts.
Come on, people!
The Osmonds!
For that to count, does there have to be someone whose last name is “The”?
Nah, I think The Osmonds doesn’t qualify. Unless they called themselves “Osmond” at one time (which would have a ring to it)
My error - I’d read somewhere that it was the middle name of one of the members.
Macklemore is a fake surname he gave himself when he was starting out. Does that count?