Non-rap examples of lyrics where the artist refers to him/herself by name

Hideous Lump brought up the B-52s upthread - add "Wig" to their resume for this one, also in the "Ready, Steve? Andy?" genre which should also include the Ramones' "Little Ramona."

Nilsson must have done this a bunch, though examples aren't popping into my mind.

In "Piano Man" we learn of a bartender who addresses the singer as "Bill."

"They Might Be Giants" and "Big Country" are borderline cases, I suppose, since they are just using these phrases in lyrics, not singing about the band.

"We've been trying to reach you, Thom"

Let's go to Luckenbach, Texas
With Waylon and Willie and the boys
This successful life we're livin' got us feudin'
Like the Hatfield and McCoys

Willie Nelson does a duet w/ Kacey Musgraves called "A Willie Nice Christmas"

I cheated on you, you cheated on me
And this is not the way that things supposed to be
So tell me girl, is this for real or just an illusion?
I pinch myself to make sure that Wyclef ain't dreamin'

Wyclef - Cheated (Rock Remix)

There was that one song on Liz Phair’s terrible s/t record where she sings “you don’t even know who Liz Phair is.”

Are you State Phair?
Are you Play Phair?
Are you Trade Phair?
Who wants to know? Who wants to know?

My wife lies down in a chair
And peels a pear
I know she's there
I'm making coffee for two
Just me and you
But I come back in with coffee for three
Coffee for three?

My dead wife sits in a chair
Combing her hair
I know she's there
She wanders off to the bed
Shaking her head
"Robyn," she said
"You know I don't take sugar!"

didn't see my favourite mentioned, from Sly's 'Thankful & Thoughtful':

someone should've come
and taken me away
but the main man thought Syl should be here another day
and that's why I've got to be
thankful/thoughtful

Girlpool - "Dear Nora"

In SF we were driving over bridges
We were singing to "I Heard It Through the Grapevine"
Cleo was tired
Harmony was hyper
We switched driving
In the middle of the highway

Blind Willie McTell. So many blues artists did this...

Answer the phone
"Harry, you're no good alone
Why are you sitting at home on the floor?
What kind of pills are you on?"
Ringin' the bell
And nobody's coming to help
Your daddy lives by himself
He just wants to know that you're well

Harry Styles • As It Was