Some bands or singers name-drop their own name in a song. Presumably* so listeners know who’s performing. I first noticed this in K-pop, but since I became aware of the idea, I hear it in R&B and rap as well. Where did it start? What band or artist did it first? And since I’m guessing it started with informal street rap, when was it first recorded?
*Comments about why they do it are welcome as well.
From TV Tropes:
MCs introducing themselves was a convention in the earliest days of late '70’s Hip-Hop, though not necessarily with the strict phrasing involved in this trope [i.e., “My name is X, and I’m here to say…”]. One example comes in “Rapper’s Delight” by The Sugarhill Gang, one of the first rap songs to gain mainstream attention, which begins with: “I am Wonder Mike and I’d like to say ‘Hello.’”
Does “Hey Hey, We’re the Monkees” count as a starting point? (1966). I bet there are earlier ones.
It’s Hammer! Go, Hammer! MC Hammer! Yo, Hammer! U Can’t touch this.
Its all about ego.
I feel like there should be some early-ish blues with singer name drops, but I’m not thinking of any off the top of my head.
I think it has to count.
Archie Bell and the Drells “Tighten Up” (1968) name drops the band in the very first line.
I can’t check right now but I believe the Fifth Dimension asks us to “sing along with the Fifth Dimension” in “Aquarius/Let the Sunshine In”
George Gershwin name-dropped himself in his 1936 song “By Strauss!”
Away with the music of Broadway
Be off with your Irving Berlin
No, I give no quarter to Kern or Cole Porter
And Gershwin keeps pounding on tin
Oh, that’s a good one!
How do you know he wasn’t talking about Ira?
Nice! But while it’s self-referential of the songwriter, it’s not really self-referential of the singer.
The term seems likely to be related to “Tin Pan Alley,” the area in New York where George (and Ira) worked composing songs. The name “tin pan” appears to specifically refer to the sound of a cheap piano; George was a pianist, while Ira was a lyricist. So, I suspect he was referring to himself.
Bach used his name as a fugue subject in the Art of the Fugue (B-flat, A, C, B-natural).
And to clarify for those who might not know, the key of B in German notation is called H, while B is reserved for what we call B-flat.
Bad Company did a song called Bad Company that included the lyric Bad Company. But it was in 1973, so no cigar.
I was leaving that as an exercise for the reader, my dear sir. 
Very early discs and records almost invariably started with the artist introducing himself and the song: “This is Harry Macdonough performing A Bird In A Gilded Cage” or “Arthur Collins here with the Metropolitan Orchestra singing My Sunflower Sue”.
But those were introductions, and not parts of the songs themselves.
None of these would be first, I know, but I can think of a few groups that referenced members in 60s songs:
“Nobody’s gettin’ fat except Mama Cass.”
“The Walrus was Paul.”
Of course, in the punk era you’ve got “Clash City Rockers” and “This is Radio Clash” among others.
And even more straightforwardly, “We Are The Clash.”
Oh, hell yes. I’m pretty sure Big Bill Broonzy referred to himself by name (“old Bill” or something similar) in a few songs, and Robert Johnson did it in Kind Hearted Woman Blues: “Makes Mister Johnson drink”