Think of Daniel Radcliffe. Is there an expression that describes his situation or state of him always being associated with Harry Potter by many people?
Typecasting and Type casting are the processes by which a particular actor becomes strongly identified with a specific character.
A quick internet search for the words: type casting and typecasting
...will find substantiation. Specific links not attached due to link degeneration.
I hope that helps.
Indelibly linked is commonly used to describe this.
And specifically talking about the Harry Potter actors: