John Cale - Mr Wilson

And, if artists count, all of Songs for Drella, of course.

They Might Be Giants -- "Meet James Ensor" (possibly fictive, but credited in the song as 'Belgium's famous painter')

La Oreja de Van Gogh is named for, well, Claude his damn self.

But bar-none, Wesley Willis owns this subject.

Randy Newman - The Story of a Rock 'n' Roll Band [about ELO]
Devendra Banhart - The Beatles
Sonic Youth - Kool Thing [LL Cool J]
Sonic Youth - Tunic (Song for Karen) [Karen Carpenter]
Righteous Brothers - Rock & Roll Heaven [buncha dead singers]
Thurston Moore - Ono Soul
The Replacements - Johnny's Gonna Die [Johnny Thunders]
R.E.M. - Lightning Hopkins
Bob Dylan - Blind Willie McTell
The Stinky Puffs - I Love You Anyway [Kurt Cobain tribute]
Richard Thompson - Roll Over Vaughn Williams
Richard Thompson - Al Bowlly's in Heaven [WWII British bandleader]
Richard Thompson - Don't Sit on My Jimmy Shands [British polka guy]
Richard Thompson - Madonna's Wedding
Richard Thompson - Dear Janet Jackson ["If you must shove your titty in somebody's face/shove it in a baby's"]
The Beatles - Savoy Truffle [supposedly about Eric Clapton's teeth]
Paul Simon - The Late Great Johnny Ace [also a John Lennon tribute]
Another dozen or so John Lennon tributes
The Bonzo Dog Band - The Intro and the Outro [namechecks lots of other musicians like Eric Clapton, the Count Basie Orchestra, and "looking very relaxed, Adolf Hitler on vibes!"]
John Cale - Legs Larry at Television Center [Legs Larry was the drummer for the Bonzo Dog Band]
John Cale - Rise, Sam and Rimsky-Korsakov
John Cale - The Soul of Carmen Miranda
Nick Lowe - Rollers Show
Nick Lowe - Bay City Rollers We Love You

Instrumentals that namecheck another artist:
Camper Van Beethoven - ZZ Top Goes to Egypt
The Velvet Underground - Booker T.

How about songs about artists' previous bands?:
Neil Young - Buffalo Springfield Again
Stan Ridgway - Talking Wall of Voodoo Blues
George Harrison - When We Was Fab

Heatmiser - Antonio Carlos Jobim
Stereolab – Brakhage
Stereolab – John Cage Bubblegum
Supergrass – Prophet 15 (references Billie Holiday and Marvin Gaye but also…Oscar Wilde, Peter Cook, Che Guevara, Steve McQueen, John Belushi and more)
Belle and Sebastian – Like Dylan in the Movies
David Bowie – Andy Warhol
Bill Ricchini – Julie Christie
Wormwood Brothers - Just Like John Lennon Said
Super Furry Animals – Shoot Doris Day