partly inspired by my current gay4jenslekman status. His song 'Black Cab' includes the line 'oh your so silent Jens'.
what other songs can you think of where the singer uses their own name or that of one of their bandmates? Or is some way sings about the fact that s/he is singing?
I can think of
'method acting' by bright eyes - where he sings to the producer to keep the tape rolling, also 'road to joy' where he sings to the band to make some noise.
'professional' by pulp - where jarvis sings 'cocker's short for sucker, a sucker of cocks'. he also uses his own name in 'i spy'.
'westie can drum' - by pavement says 'westit cannot drum' bizarrely.
sufjan has his 'collection of drones representing how sufjan stevens etc etc' on illinois. that kind of counts too...
anyway I'm sure there are loads of these.