I can only think of three bands that take their name from one of their songs: Bad Company, Black Sabbath, and Rammstein.
There’s gotta be more…what are they?
Big Country - “In a Big Country”?
Deicide, off their self-titled album.
Madness.
Jilted John.
King Crimson (“In the Court of the Crimson King”)
Do the Clash (“Clash City Rockers,” “This Is Radio Clash”) count?
Iron Maiden
Exodus
Only if you include Queen/ Killer Queen.
Forgot to add:
Iced Earth
Well, Helloween had a song called “Halloween”, maybe this could be a sub-group of close calls. 
D
Motorhead
Wang Chung “Everybody have fun tonight, everybody Wang Chung”
Talk Talk
Belle and Sebastian
That was supposed to beTalk Talk.
Hmm, The Soft Boys had “Give It to the Soft Boys.”
They Might Be Giants named after themselves. It speculates that they might be really big jerks.
Named a song after themselves.
It’s neat when your sentences make sense.
Bad Company had a song called “Bad Company” on the “Bad Company” album.
Around 1971, there was a group called the Sweet Inspirations (which included Whitney Houston’s mother - Cissy Houston) and their biggest hit was called “I Need Your Sweet Inspiration”.
Green Day (“Green Day” on 39/Smooth album) who were also previously called Sweet Children (“Sweet Children” on the Sweet Children EP)
Spacehog
Living Colour
Public Image by PIL
Theme From The Monkees by The Monkees
Jocko Homo by Devo self-refers in the chorus.
The Clash have at least two, though I dislike both of them intensely.
Oops! The 2 Clash songs I don’t like are This is Radio Clash and We Are The Clash. I forgot about Clash City Rockers, which I like. :smack:
Stray Cats - “Stray Cat Strut”
Escape Club - “Wild Wild West” (self-reference in the song)
As far as self-references in songs go, I’m sure that there’s a ton of rap and hip hop tracks that could be listed here. (No, I’m not going to start listing them. I don’t follow the genre, but I’m sure that I’ve heard it many times when I’ve bothered listening to the lyrics.)