Dr. Hook and the Medicine Show’s The Cover of the Rolling Stone starts with someone saying “Hey Ray, hey Sugar, tell 'em who we are!” Ray is band member Ray Sawyer. I’m not sure who Sugar is.
Jethro Tull had several songs that alluded to “Jeffrey.” That was former band member Jeffrey Hammond (Ian Anderson renamed him Jeffrey Hammond-Hammond). Among the tunes: “Jeffrey Goes to Leicester Square,” “A Song for Jeffrey,” and “For Michael Collins, Jeffrey and Me.”
George Harrison wasn’t in the Beatles any more when he wrote “Living in the Material World,” but the lyrics allude to “Richie” (Ringo).
Bruce Springsteen’s “10th Avenue Freeze-Out” is about the formation of the E Street Band, and while it doesn’t say Clarence Clemons’ name, it alludes to “the Big Man.”
In the Bob Dylan parody “A Simple Desultory Philippic” by Simon and Garfunkel, the lyrics say " I’ve been Mothered, Fathered, Aunt & Uncled, Roy Haleed and Art Garfunkeled." (Roy Halee was their producer.)
“The Absence of God” by Rilo Kiley names a few people who are band friends, not members, but… Mike, I’ll teach you how to swim
If you turn the bad in me into good again
…was Mike Bloom who did a stint with the band during that album period.
Now that I mention it, “Papillon” has the line “Oh my God, Blake” in reference to band member Blake Sennett.
I don’t know if it counts, because technically it’s not part of the lyrics, but in Neil Young’s “Speakin’ Out” from Tonight’s The Night, just before Nils Lofgren’s solo Neil says “Alright, Nils, alright”.
In "The Bride Stripped Bare by ‘Bachelors’’ by the Bonzo Dog Band, the lyrics mention band members “Legs Larry” (Smith), Mr. (Rodney) Slater, and Neil (Innes).
Another of their songs was “Mr. Slater’s Parrot.”
“My Pink Half of the Drainpipe” has the lyric “Rodney’s bass saxophone solo as promised.”
And, of course, “The Intro and the Outro” introduces all the members of the band: Vivian Stanshall, Neil Innes, Legs Larry Smith, Vernon Dudley Bohay-Nowell, Sam Spoons, Roger Spear, Rodney Slater, John Wayne, Robert Morley, General de Gaulle, Adolph Hitler, Liberace, Eric Clapton . . . .
Pete played on the bass guitar
Liked to get around, mixing with all the stars
But Mrs. Avory’s child was all fingers and thumbs
But solid as a rock, setting time on the drums
While Dave the Rave hit the rock ‘n’ roll riffs
Yours truly strummed away with a slightly limp wrist
From They Might Be Giants’ “They Got Lost”:
John said to John
“I think we make a left at the light
There should be a big ‘B’
assuming this map is right”
John looked over and he said,
“Hey, no it’s not
It’s a crumpled up wrapper
From the fast food that we got”
The Eighties incarnation of King Crimson had a novelty song called “Crimson Barbershop,” which mentioned all four members of the group by name (bassist Tony Levin did all the vocals by himself).
“I’m Tonyyyyyyyy
I’m Billyyyyyyyy
I’m Bobbyyyyyyy
I’m Belew.
We’re here to sing and play for you
Oh we’re the King Crimson band – and don’t you know it
We’re the best in all the land – all the land
We play bass and the drums and guitar for you
And if you really want we’ll throw the Stick in too
Oh we’re the King Crimson band (on EG Records)
And you know we think that’s grand
So settle back to have some fun
And tap your foot in 21.”
“The Ballad of Mott the Hoople” contains these lines
“Buffin lost his childlike dreams
And Mick lost his guitar.
And Verden grew a line or two
And Overend’s just a rock & roll star.”
Dale “Buffin” Griffin was their rummer, Mick Ralphs was their guitarist, Pete “Overend” Watts was their bassist, and Verden Allen was their organist.