Word for "An expression or saying one uses so much that it comes to define them" [duplicate]

Catchphrase would fit the first sentence.

I don't see how the word you ask for in the first sentence would fit the second sentence.


Shtick

one's special trait, interest, or activity : BAG

He's alive and well and now doing his shtick out in Hollywood. — Robert Daley

[Merriam-Webster]