No, I haven't heard any such song that represents my entire true identity.

Bad guy by Eminem probably

The song "Water Woman" by Spirit (also covered by one or two other bands) has a lyric that represents my true self:

"Water's the only way, water's the only way, follow the fish today, see what he has to say".

You see, I [i]am[/i] the fish.

[youtube=https://www.youtube.com/watch?v=u9Dg-g7t2l4]

"Sweet disposition" the temper trap

"Born Losers" by Matthew Good

Psychidelic Souljam

Nope.

[youtube=https://www.youtube.com/watch?v=E3AeYeFHMB4]

😁 ☀