When a poem praises a loved one piece-by-piece, it’s called a blazon.
Is there a name for a poem/song that extols one’s *own *virtues and accomplishments, though? There must be, because there are a lot of popular songs in this form. *Rodomontade *and *braggadocio *come to mind, but neither refers specifically to poetry/song lyrics.
Help?
According to Icelandic poet and philolologist Jón Helgason, it might rightly be known as a Peire Vidal- poem, after the old Occitan trobadour.
Jón even made a (second-hand) translation of some of Vidal’s verses, and they seem to stand the test…
And the earliest known example is - Celtic Boast Battle! 
Since this is about literature, let’s move it to Cafe Society.
Colibri
General Questions Moderator
This is the first time in fifteen years a thread I began has been moved to a different forum. I guess I’m really starting to fit in?
Curriculum vitae? What? It doesn’t rhyme, but it has a highly constrained format and a prescribed length. It’s like a haiku, but because your future is depending on it, the stress is on every syllable.
Well played. Unfortunately in my years in academia I never saw a CV that I’d call poetry 
Ben Jonson wrote a poem called “Ode to Himself”.
Possibly a Balliol Rhyme.
My name is George Nathaniel Curzon
I am a most unusual person
My cheeks are pink , my hair is sleek
I dine at Blenheim twice a week
Apologies. Please substitute "superior " for “unusual”