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

The Roches - they'll tell you their names but they won't give out their phone numbers

https://www.youtube.com/watch?v=oZ8MdYsgELs

Another Alexander O'Neal one, from In the middle:

Some people are satisfied
Living and loving on borrowed time
But if you can't be my own baby
All you have to do is say
Alex darling (doesn't?) play it that way

The Floaters - Float On

Almost every post-1975 Jonathan Richman song

Lambchop - "Kurt Wagner's Heart Attack"

Always loved this bit from "I Think She Likes Me" by Treat Her Right (Mark Sandman's pre-Morphine band)

"She listens to every word I say
I look at her she don't look away
I tell her that I play for "Treat Her Right"
She asks me if I'm gonna play tonight - Yeah!"

From Jarvis Cocker's lyrics/vocals for Barry Adamson's 'Set The Controls For The Heart Of The Pelvis'

Ahhh, can't you see what's on offer
Yeah babe it's going cheap today
I enter a room and all the girls say
C'mon Jarv, can I be the first?
Oh you make us so hot we feel we're gonna burst

She said Paul, you better look around
How long you think you can run that body down?
How many nights you think that you can do what you been doin'?
Who you foolin'?

--"Run That Body Down" (P. Simon)

"Boogie down with Davy now" from Bowie's 'John I'm Only Dancing Again'.

Old hat for Bowie, really -- from the mid-sixties, "Can't Help Thinking About Me":

"Now I leave them all in the never never land
The station seems so cold the ticket's in my hand
My girl calls my name, 'Hi Dave.
Drop in, see around, come back
If you're this way again.'"

I feel like this was a common device in old-school indiepop, but I can only think of a couple (non Jonathan Richman) examples:

Heavenly - Escort Crash on Marston Street

Hey now, Robert, you happy with your smashed up car
And your broken neck bone, and your facial wounds?
You've murdered Amelia. Pete can no longer play guitar
And Mathew's brain is damaged. But that's not so different
Could you tell at all?

and All Girl Summer Fun Band - Grizzly Bear

We all know that you can't always do what you feel
But if you know exactly how you feel, you can always come and tell me say,
"Hey Kim, I'm kind of feeling like a grizzly bear
Yeah, I feel like a grizzly bear,
I want to roll on the ground and I want to mess up your hair"

Learned about this one from the "You Must Remember This" podcast -- second episode ever! (And this song is not a joke -- I'm only quoting the first part of it, it gets crazier from there.)

https://www.youtube.com/watch?v=xCCw6gYEeKw

― Ned Raggett, Wednesday, December 7, 2016 12:53 PM (two months ago)

I like the one that goes

I'm Frankie Sinatra
I'm Frank Sinatra
I'm Frankie, me boy, you don't know
I've got the perfect voice to sing calypso

srsly though, thanks for sharing that, it's nuts

My favourite example of this ever: Goddo's "Sweet Thing."

youtube.com/watch?v=-2GK1jxvroE

"You like the fact I'm in the Goddo band / You're aware of a one-night stand."

(Didn't embed the video, so don't complain to me.)

"They call me, Dr. John, The Night Tripper"

Another Bowie, "Teenage Wildlife":

Same old thing in brand new drag comes sweeping into view
As ugly as a teenage millionaire pretending it's a whizz kid world
You'll take me aside, and say
"Well, David, what shall I do? They wait for me in the hallway"
I'll say "don't ask me, I don't know any hallways"
But they move in numbers and they've got me in a corner
I feel like a group of one, no no they can't do this to me
I'm not some piece of teenage wildlife

The Mighty Sparrow - Sparrow Dead

(he probably does this a lot but that's the one that immediately sprung to mind)

Belle & Sebastian - "This Is Just a Modern Rock Song"

Stevie's full of good intentions,
Richards into rock 'n' roll,
Stuart's staying in and he thinks it's a sin,
That he has to leave the house at all.

Electric Light Orchestra - "Shine a Little Love" (cued up: https://youtu.be/GJuTIxwQw0k?t=3m38s)

You shine a little love on my life
(Shiii-iii-iiine)
You shine a little love on my life
(E-L-O)
You shine a little love on my life and let me see

The Floaters - Float On

― MarkoP, Wednesday, December 7, 2016

And the song it inspired, The B-52s - "Song for a Future Generation"

Speaking of whom, also "52 Girls" namechecks Kate and Cindy.

No Bad Religion song can make your life complete ("No Direction")

Alice Cooper - "Be My Lover"

"she asked me why the singer's name was Alice, I said listen baby, you really wouldn't understand"

Jacques Brel, "Jackie"

Another one:

https://www.youtube.com/watch?v=OAZwnl6UAig

Jacques Brel, "Grand Jacques"

Jerry Lee Lewis is the master of this
― Brad C., Wednesday, 7 December 2016 15:40 (two months ago)

Best example, "Lewis Boogie":

"My name is Jerry Lee Lewis, come from Louisiana
I'm gonna do you a little boogie on this here piano"

Mary J Blige x2

Doesn't matter if you're white or black
Let's get crunk cause Mary's back
(Family Affair)

Deep inside I wish that they could see
That I'm just plain ol' Mary, Mary (and throughout much else of the song)
(Deep Inside)

Anoter Lennon one on "God" :
"I was the Walrus but now I'm John"

oh and also in "Give Peace A Chance" : "Ev'rybody's talking about
John and Yoko"

Beyonce certainly has plenty !

Me and Mike Watt playing the guitar

Another indie-one, from Laakso, led by Markus Krunegård.

A junkie, an addict, a slave for your love
But I'm not in love
I'm just obsessed
With hearing you say "yes please Markus come to me"

"Heathcliff, it's me, Cathy"

Beyonce certainly has plenty !

Kelly, can you handle this?
Michelle, can you handle this?
Beyoncé, can you handle this?
I don't think you can handle this!

http://i.imgur.com/gKPi3cp.jpg, it's me, http://i.imgur.com/zLRm67S.png

(some people say 'Wuthering Heights' is about a really old book, but I don't think that's true...)

'Jesus? This is Iggy.'

(Sorry, from 'Turn Blue'.)

Cheap Trick, "Surrender"

towards the end: "Robin's alright, Tommy's alright, Bun E's alright, Rick's alright"

mandy moore "candy"

There's that one of the fifty-billion versions of "Two Tribes" where they do a roll call before "Mine is the last voice that you will ever hear."

No my first name ain't baby
It's Janet
Miss Jackson if you're nasty

Beatles - Glass Onion

"...the walrus was Paul..."

White Stripes - It's True That We Love One Another

...I love Jack White like a little brother.

There must be more by them, I feel like Jack White talks about himself a lot

Beatles - Glass Onion

"...the walrus was Paul..."

that was John singing, though.

Jonathan Richman thirded. Also came to mention some additional Lou Reed, from "Coney Island Baby," but it was already mentioned on this similar thread: Songs where the singer mentions his own name

Said Captain, said WOT?

although, that's rap, I guess...

https://www.youtube.com/watch?v=8_YYC2N_lxY

also: michael chapman - wrecked again... & i seem to recall lee hazlewood did this on occasion

Stevie Wonder - Please Don't Go

so baby please don't leave
don't leave Steve

Pet Shop Boys - Single Bilingual

and after work explain how I feel
"Perdóneme, me llamo Neil"

Kevin Barnes from of Montreal does this a fair bit.

The voice said, "Don't worry, friend
The darkness is just a suggestion
No, don't worry, kid
The darkness is just suggestion
No, don't worry, Kevin"

Serge Gainsbourg has done that a lot (even a whole album : "L'Homme A Tête De Chou" !)

So basically, as this thread proves, it's a common songwriting trick.