The first three albums by Focus included songs called “Focus,” “Focus 2,” & “Focus 3.”
Iron Butterfly had “Iron Butterfly Theme.”
Not a band, but Van Dyke Parks recorded “Van Dyke Parks.”
How about Can’s “Can Can”?
Halfway there: first song on the first Gentle Giant album was called “Giant.”
“Love Theme From Kiss” - Kiss
“Butthole Surfer” - The Butthole Surfers
“Stray Cat Strut” - The Stray Cats
“Bo Diddley” - Bo Diddley
“Hey, Bo Diddley!” - Bo Diddley
“Diddley Daddy” - Bo Diddley
“Run, Diddley Daddy” - Bo Diddley
“The Story of Bo Diddley” - Bo Diddley
“Bo Diddley 1969” - Bo Diddley
“Bo Diddley Vamp” - Bo Diddley
“Bo’s Beat” - Bo Diddley
“Bo’s Guitar” - Bo Diddley
“Bo’s Waltz” - Bo Diddley
“Bo Diddley’s Dog” - Bo Diddley
“Bo’s a Lumberjack” - Bo Diddley
“Art In America” by Art In America.
“This is Cracker Soul,” by Cracker.
Madness (the band) is named after a Prince Buster song, which they covered.
They also later wrote and recorded a song called “Madness Is All In The Mind.”
While we’re at it, Sisters of Mercy were named after a Leonard Cohen song, which they have also covered (at least in concert.)
Who Are You? by the Who–does that count?
Also Wang Chung mentions themselves in “Everybody Have Fun Tonight.”
KMFDM has a song called “Sucks” which goes, in part “KMFDM SUCKS!” Not a 100% match to the OP…
The Dead Milkmen have the “Milkmen Stomp”
Belle & Sebastian have a song called “Belle & Sebastian”
Jerry Lee Lewis had the Lewis Boogie
From the 11th album:
Take Me Back To Chicago by Chicago.
“They’re Red Hot” is a cover of a Robert Johnson song.
In 1987, Living In A Box reached #17 on the US pop chart with their song “Living In A Box”, from their album Living In A Box. (I don’t remember ever hearing the song, but I remember wondering how many times that had happened.)
“Young Fresh Fellows Theme” by the Young Fresh Fellows.
Damn, this was a great band. That no one remembers. Click on some of the samples.
And I just remembered:
Killer Queen by Queen.
Since a lot of these songs appear on the bands’ debut albums, it makes me wonder which came first: the song title, or the band name. I tend to think that a lot of these bands had really stupid, or at least unmarketable, names when they got signed, and a record company person pointed to the song title and said, “But that sounds cool. We’ll call you that.”
Not exact matches, but “Freezepop Forever” and “Parlez-vous Freezepop?” by Freezepop.
“Supersucker Drive-By Blues” - The Supersuckers
“Wu-Tang Clan Ain’t Nuthing ta F’ Wit” - Wu-Tang Clan
“Wu-Tang: 7th Chamber” - Wu-Tang Clan
“Wu-Tang: 7th Chamber - Part II” - Wu-Tang Clan
“As High As Wu-Tang Get” - Wu Tang Clan
“Who Are We? (The Dixie Hummingbirds)” by The Dixie Hummingbirds.
From the late 1960’s “(I Need Your) Sweet Inspiration” by the Sweet Inspirations (which included Cissy Huston - Whitney’s mom).
The Butthole Surfers are one of the bands that did it the other way around. They used to go by a different bizzare and hilarious name every show (my favorite of which was “Nine Foot Worm Makes Own Food”), but they had a popular song called “Butthole Surfer.” Soon everyone was calling them “that ‘Butthole Surfer’ band” or “The Butthole Surfers” and they just went with it. Oddly enough, the song wasn’t on their debut EP.
“Hellyeah” by Hellyeah