Songs whose lyrics mention the band's name...

...but aren't self-titled songs (IE: Bad Company - "Bad Company") or mentioned in the song's title (IE: Queen - "Killer Queen"):

Boston - "Rock N Roll Band"
The Fifth Dimension - "Aquarius/Let the Sunshine In"
Yes - "Tempus Fugit"

Others?

 

Steely Dan "Show Biz Kids"
Chic "Le Freak"

 

Wilco the Song by Wilco

 

"we were just another band out of Boston...." - that mentions the city, not the band.

 

Utopia Theme - Utopia
My Name Is Prince - Prince (or TAFKAP)

 

Beastie Boys "Fight For Your Right"

 

Kinda along those lines..... How about when Freddie M says "Down in the city, just Hoople 'n' me..." in 'Now I'm Here'. Close enough?

 

Ah!

I Go Crazy - Queen ("I don't wanna go see Queen no more")

 

Iggy Pop: "Turn Blue" ("Jesus? This is Iggy...")
John Lennon: "God" ("I don't believe in Beatles")

 

"To the sound, of old T Rex, and Who's Next". The Who "You Better You Bet"

 

And pretty much every Hip-Hop song from that era, right?

 

This doesn't count, but when I first heard Sgt Peppers I used to think Paul was saying "see the Beatles standing there" on Fixing a Hole. >.<

For a real one, The Honeys - Shoot The Curl.

 

"Gotta Serve Somebody"

You may call me Bobby, you may call me Zimmy

 

"Jocko Homo"

Are we not men?
We are DEVO!
Are we not men?
D-E-V-O

 

Ray Charles "Don't You Know" (and he mentions at least his first name in a few others)

 

It's a good thing I don't know all that much hip-hop, huh?

 

Shiny Toy Guns-When They Came For Us

 

"Calling Dr. Love" by Kiss:

"The first step of the cure is...a kiss"

 

"Give It To The Soft Boys."

.

 

"Creeque Alley" mentions Mama Cass, if that counts.

 

Vengaboys, "Boom Boom Boom Boom."

 

"The Hop" Aerosmith:

"'Cause you'll be kickin' [butt] tonight with the boys in Aerosmith"

 

Ice Ice Baby Vanilla, Ice Ice Baby Vanilla

 

The Clash - We are the Clash

Bowie if you include his pseudonym -
Ziggy played guitar, jammin' good with Weird and Gilly,
The spiders from Mars, he played it left hand...

Alice Cooper - Be My Lover

 

There are numerous songs in which the band or artist only mentions a part of his name, such as Billy Joel in "Piano Man." Do those count?