There’s the song “Wilco” by the band Wilco on the album “Wilco.”
The E Street Shuffle. Sort of. I’ll allow it.
Motörhead by Motörhead. Lemmy had written the song for his former band Hawkwind, but they hadn’t recorded it when he got kicked out of the band. So he took the song for his new band which he called after the song.
Belle And Sebastian - Belle And Sebastian.
Actually, Hawkwind did record it, with Lemmy on vocals even.
Well, I didn’t know that. Was it officially released back in the day or only later?
It was on Warrior at the Edge of Time, the last album they did with Lemmy.
Thanks for the correction and the link. 
ETA: is that a violin? Never would have thought that a Lemmy song worked with strings.
Came to write Motörhead, have discovered an earlier version called Motorhead, not yet with an ö but with an o. Things you learn on the Dope 
Will add Ziggy Stardust by Ziggy Stardust and the Spiders from Mars, and Aladdin Sane by Aladdin Sane. Perhaps they count.
Madness is named after a song by Prince Buster, which they covered.
Minor nitpick, it’s “Wilco (The Song)”, from the album “Wilco (The Album)”.
Though not a big chart hit, the first single I recall hearing on the radio by Kool and the Gang was titled “Kool and the Gang” in 1969.
Not a perfect name-title match, but the Rolling Stones have covered Bob Dylan’s “Like a Rolling Stone.”
Even more of a reach, King Crimson’s “In the Court of the Crimson King.”
KMFDM does not, but they mention themselves a lot in their songs. Like, each album has a song that that mentions themselves in comical ways, disparaging or even calling themselves awesome in an obviously sarcastic way.
Focus also had a song “Focus,” plus “Focus II, “ “Focus III,” and “Focus IV.”
The Monkees sang a song that’s often referred to as “Hey Hey We’re The Monkees”, although it’s title is technically “(Theme From) The Monkees”.
Stars on 45 on the album Stars on 45 by the studio cover band Stars on 45.
To get just a little meta, there’s Johnny B Good, Sultans of Swing and St. Pepper’s Lonely Hearts Club Band. I know what you’re thinking…”Those performers didn’t perform the song.” No, but the musicians did perform in the song. You can hear them playing. Chuck Berry, Dire Straits and The Beatles each show you what their song sounded like, so therefore the song Sultans of Swing is at least in part by the Sultans of Swing.
Contrast this is the Devil in Devil Went Down To Georgia. “It sounded something like this.” But the song name is neither Devil nor Johnny, so it doesn’t count.
Public Image by Public Image Ltd
Blockheads by Ian Dury And The Blockheads
j
The first one that came to mind.
And a near miss:
In A Rut by The Ruts
j