Now here’s a little story I’ve got to tell
About three bad brothers you know so well
It started way back in history
With Adrock, (M.C.A.) and me (Mike D.)
R.A.M.O.N.E.S sung by Motorhead and the Ramones:
*Bad boy rock, bad boy roll,
Gabba gabba, see them go,
C. Jay now hit the gas,
Mark takes it up the ass,
Go johnny go go go
Tommy o-way-o
[chorus]
Bad boys then, bad boys now,
Good buddies, mau mau mau,
Keep it up, rock n roll,
Let the music save your soul,
Dee dee, he left home,
Joey calls me on the phone.*
Also by the Ramones “It’s Gonna Be Alright”
Got good feelings about this year
All is very well, C.J. is here
Crazy Little Thing Called Love by Queen
“Because I’m ready (Ready Freddie)”
One of Queen’s last singles, “The Invisible Man”, includes the full names of all four band members, as shout-outs in between the verses. (The video feels, to me, like a clip from a bad “Doctor Who” episode. 
)
On Electric Light Orchestra’s “Easy Money,” just before the guitar solo (at 1:28), Jeff Lynne says, “Take it, Jeff!” (An inside joke, since, by that point, ELO was essentially a Jeff Lynne solo act, and he was telling himself to “take it.”)
Chanitllly Lace - “This is the Big Bopper speaking…”
How dare you make that prejudiced generalization before I had the chance to, not like it didn’t make a SNL skit last week or anything!
Do shout-outs (“Play a guitar solo now, fellow band member!”) count as being part of a song’s lyrics?
The Floaters “Float On”
My favorite lyric:
“Cancer and my name is Larry, huh
And I like a woman
That loves everything and everybody”
“We’re Archie Bell and the Drells from Houston, Texas! We don’t only sing, but we dance just as good as we walk!”
Tighten Up!
Marky Mark and the Funky Bunch Good Vibrations
“Donny D’s on the back up.
Drug free, so put the crack up”
OMC’s How Bizarre mentions backup singer Sina, and somebody named Pele several times.
The Time Jungle Love
“Jesse… now Jerome
O! E! O! E! O!”
ABBA’s I Am An A
Also on Motley Crue’s “Girls, Girls, Girls”:
Tommy, check that out! /
Where, Vince, where?
We are Maggi and Terri and Suzi,
Maggiiii and Terriiii and Suziiiiii Roooooche…"
– The Roche Sisters (“We”)
“The Seether’'s Louise.” - Veruca Salt, referring to guitarist Louise Post. (Who I went to High School with, which you need to know for no reason)
Marilyn Manson calls Brian Warner (his real name) the N word in his cover of Patti Smith’s Rock ‘N’ Roll Nigger.
Eminem song Marshall Mathers.
One I’m surprised hasn’t been mentioned yet:
“It’s Janet, Miss Jackson if you’re nasty.”
Does “Mr Mojo Risin” count?
I don’t know how close to the topic this gets, but in Joe Walsh’s solo song Shut Up, he mentions two of his bandmates in the Eagles.
Hank Williams, Jr - Family Tradition
“Hank, why do you drink?
Hank, why do you roll smoke?
Why must you live out
The songs that you wrote?”
I always figured that “Take it Jeff!” was a throwback to the old Move song “California Man” where Roy Wood tells Jeff Lynn to “Take it, Jeffrey!” Actually I think there were a couple of Move songs where he shouts that.
Billy Joel, “Piano Man”: “He said, Bill I believe this is killing me…”
Rick Springfield, “Bruce”: “My name is Rick, I’m gonna stick it to ya babe…”
“…Sincerely, L. Cohen”
Leonard Cohen, “Famous Blue Raincoat”.
Just walking through the set, drunk as they could get
And what the hell was wrong with Joe?
Local H, “All the Kids Are Right” (referring to band member Joe Daniels)