It came to my attention today that the band Nazareth, which I always assumed named themselves after the Biblical city, actually took their name from a line in the song “The Weight” by The Band.
Source: Wikipedia
What other bands chose their name from other people’s songs? I added the word “unrelated” in the title so as to intentionally exclude tribute bands and the like, which I believe do this all the time.
Boys Don’t Cry, after the Cure song.
Death Cab for Cutie, from the name of a song by the Bonzo Dog Doo-Dah Band.
Death Cab For Cutie was named for a song by the Bonzo Dog Band.
Godsmack named themselves for a song by Alice in Chains.
Lady Gaga says she came up with the name from Queen’s “Radio Ga Ga”.
Radiohead named themselves after a song by, I think, the Smiths.
Didn’t the Rolling Stones name themselves after Dylan’s “Like a Rolling Stone”?
Deacon Blue took their name from a Steely Dan song.
Steely Dan took their name from an, …ahem… appliance in a Edgar Rice Boroughs novel.
Actually, Muddy Waters’ “Rollin’ Stone.” Similarly, The Pretty Things took their name from a Willie Dixon song.
No, from Muddy Water’s “Rollin’ Stone.”
Talking Heads. But good one!
Wow, I just came in to mention Eric’s Trip…I thought I was about the only Doper who knew about them.
Cocteau Twins took their name from a song by Simple Minds.
There’s always Toad the Wet Sprocket, who got their name from a Monty Python skit called “Rock Notes”, which is a music news broadcast which mentions a number of fictional bands, one being Toad the Wet Sprocket.
Reginald Dwight took his stage name in homage to Bluesology saxophonist Elton Dean and Long John Baldry. He’s known today as Dean Long. 
And Declan Patrick MacManus took the name stage name Elvis Costello, with the first name…well, you know.
Dixie Chicks took their name from the Little Feat song and album Dixie Chicken.
Hmmm… I seem to have confused “bands taking their names from songs by other bands” with “artists taking their names from other artists.”
Anyway, at this site http://library.thinkquest.org/4626/rock.htm it says Simple Minds were named after a line in the David Bowie song “Jean Genie”.
Not Edgar R. … William S. Naked Lunch, not Naked Ape-man
ETA: Oops. gregorio got it first.
The Moody Blues took their name from the Duke Ellington song “Mood Indigo.”
Deep Purple were named for the old standard, “Deep Purple” (When the deep purple falls/over sleepy garden walls . . . )
Madness took the name of a song by Prince Buster.
Adam Again were named after an album/song by Michael Omartian.
Just going from memory:
Pretty Boys Make Graves
Panic! at the Disco (they claim not to be. But I always think they are)
Boys Don’t Cry
Scar the Armada
Dear Ambellina
Maria Mystar
(The last three are from Coheed and Cambria lyrics. and then there IS the tribute band “Two Among the Fence” but per the OP that doesn’t count)
Milks and Rectangles - from Avalanches (Frontier Psychiatrist)
The Telephone Junkies - from Elvis Costello
Blood on the Dancefloor - from either Panic! at the Disco or Michael Jackson
One presumes that Aqualung got the name from the Jethro Tull song. And a now disbanded indie band called Blood on the Tracks is most likely named after the song by Bob Dylan. HelloGoodbye is named after The Beatles song “Hello, Goodbye.” And Seether is named after the Veruca Salt song.
Pretty sure you meant Pretty Girls Make Graves, Ludovic.