What they call you

[Glen]

Lucille Clifton said

What they call you is one thing. What you answer to is something else.

What is the best way to express that?

Una cosa es lo que te llaman, y otra cosa es a lo que respondes (?)
No importa qué te llaman [¿llamen?], sino a qué nombre respondes (?)
?

[AngelicaDeAlquezar]

Hmmm... the first part of your proposal is not exactly wrong, but it doesn't sound natural for me... (the second part is alright, but less colloquial than what comes to my mind at first.)

I think I'd say something like "Una cosa es cómo te digan ("llamen" might work, but I don't like the sound of it for this context) y otra distinta es a qué haces caso / a qué contestas".