Hmm, not sure if obviously adopted last names should count.
This might be my favorite example - it just drips with arrogance / confidence.
The lead singer and the bass player of UFO, Phil Mogg and Pete Way, released a couple of albums as Mogg/Way.
TCMF-2L
Couple lesser known rock bands…
Keel - named for singer Ron Keel
Impellitteri - named for guitarist Chris Impellitteri
Obviously Bachman Turner Overdrive doesn’t count but I believe after they broke up two of the band recreated as Bachman & Turner which does.
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Brothers and drummers Vinnie and Carmen Appice released an album together as Appice.
However while Carmen has released albums under his own name he also has used band names:
**Beck, Bogert and Appice
Char, Bogert and Appice**
**Derringer, Bogert and Appice
Travers and Appice
Vargas, Bogert and Appice **
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Based on OP and subsequent judicial rulings, it appears that the sole permissible word other than surname(s) is “and”?
The five Tavares brothers perform and record as Tavares.
Tragically, Sleater-Kinney is named for a road sign.
Perhaps not exactly what the OP is looking for, since it also involves the first and middle names of one band member (but not his last name), but back in the 1970s, there was Hamilton, Joe Frank and Reynolds.
The band was made up of Dan Hamilton, Joe Frank Carollo, and Tommy Reynolds.
Mouth and MacNeil. Assuming stage surnames count.
If we have arrived at ‘near misses’ I had thought of the band name and album by some of the members of Free called Kossoff, Kirke, Tetsu and Rabbit. Although Tetsu is the bass player’s first name he is Japanese so I assume it is his family name / surname. Academic though since ‘Rabbit’ is the keyboard player’s nickname.
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McFadden & Whitehead of ‘Ain’t No Stopping Us Now’ fame.
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Forget about Coverdale*Page - which should be a solid black circle not an * but sadly I don’t know how to do it. You forgot the (even more prestigious?) Page and Plant which Jimmy and Robert used for a while after their Led Zeppelin days.
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Unlikely. I will not say definitively that Tetsu is never a family name, but it’s mostly a given name. (Checking, his family name is Yamauchi, and his full given name is Tetsuo. Interestingly, he writes the short version in katakana, which is unusual for a totally ordinary Japanese name…)
Thanks for all the interesting references - and TCMF-2L, that is some really impressive expertise!
So this definitely sounds like a convention that peaked in the 70s-80s and mostly limited to certain genres of music.
Yup, I guess that about sizes it up. 
Another Yes reshuffle resulted in Anderson, Rabin, and Wakeman.
I was going to suggest his name in the band is likely merely part of a longer given name, therefore a nickname, that is something like a counting prefix. The roots of Japanese counting go way back to a different set of words than were adopted from the Chinese.
Roughly translated they would be…
1 = Hi
2 = Fu
3 = Mi
4 = Yo
5 = Itsu
6 = Mu
7 = ??
8 = Ya
… [Japanese/Vocabulary/Numbers - Wikibooks, open books for an open world]*
And one of my English students in Japan said his name, Tetsuhiro, translated into Seventh Son and, when I noted how lucky it’s supposed to be to be a seventh son, he shook his head and said no, his parents were joking around with naming him and the characters are actually Seven Sun (or Seventh Sun, or Seven Suns, or – well, whatever it meant was tougher to figure out than the translation). Typically, “son” is the character chi {first son} or ji {second son} or…
Anyway, the point is that, while I don’t know what character Mr. Cave (Yamauchi-san) uses for the O, his name would seem to be shortened to “Tetsu” for his bandmates convenience and it would therefore make sense to be written in katakana, which is used for terms that come from outside of the Japanese language.
Bon Jovi, by the way, is the fan-friendly version of Jon’s family name, Bongiovi.
–G!
*I found it curious that the list above skips number seven and nine.
Medeski Martin & Wood
I have clearly humiliated myself with Kossoff, Kirke, Tetsu and Rabbit.
To redeem myself I offer Arthur Buck. A collaboration between Joseph Arthur and **R.E.M. **guitarist Peter Buck which produced one self titled album.
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Fairly successful 1970s duo Seals and Crofts comprising James Seals and Darrell Crofts.
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Too late to delete this post but they were mentioned up thread.
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