Four U.S. Billboard Hot 100 “One Hit Wonders”:
Brewer & Shipley (“One Toke Over the Line”)
Ray, Goodman & Brown (“Special Lady”)
Yarbrough & Peoples (“Don’t Stop the Music”),
Zager & Evans (“In the Year 2525”)
Bell Biv DeVoe may count, although “Biv” was a truncation of “Bivins”.
An obscure one but Robert Allen is vaguely connected to the much better known Depeche Mode.
Robert Allen normally styles himself **Robert Marlow **and as a solo artist has released records under that name. But he also partnered with Gary Durrant for an album as MARLOW (in uppercase.)
TCMF-2L
And after The Osmonds broke up, the guy got together with a relative and formed The The.
Emerson Lake & Powell
Peaches and Herb. Pick any of the several Peacheses.
Jazz greats Lambert, Hendricks, and Ross. When Ross left, they became Lambert, Hendricks, and Bavan.
Flanders and Swann
“The Gas Man Cometh” – - YouTube
I had a look on Wiki and “Peaches” is merely a nickname (for the first of several women) while “Herb” is the guy’s first name.
TCMF-2L
Womack & Womack - Husband and wife duo of Cecil and Linda. Had a few hits.
TCMF-2L
Flanagan and Allen comprising Bud and Chesney but I am not sure Music Hall acts are “bands” in the sense the OP means it.
TCMF-2L
How about Was Not Was?
Giles, Giles and Fripp
I should have known Vandenberg featuring Adrian Vandenberg - known for the single “Burning Heart”
Rick Derringer at one point also had a band just called Derringer. Vinny Appice was in it.
Souther–Hillman–Furay Band, if you’re allowed to have Band in the name.
I’m not sure that we should count bands that use multiple surnames. It doesn’t seem to fit with the title of the post.
Have I missed Carpenters? (There’s no “The” in it.)
How about** The McGarrigles**? (There IS a “The” in this one.)
I don’t think assumed names count.
Thanks but in fact I was thinking about band names that only use the surname without any adornment… so “Carpenters” wouldn’t count but “Carpenter” would. And yeah, I don’t think obviously fake last names count. I’m ok with multiple plain surnames though. (eg, “McFadden and Whitehead”)
BTW, I’m loving some of the obscurities dredged up in this thread - hard to believe stuff like “Arthur Buck” or “Marlow” really existed 
More Yes Shinanigans
Bruford had a band called, you guessed it, Bruford
McDonald and Giles, which is made up of the surnames of the three members of the band.