Would it be correct to also say ¿Cómo te llamas tú? or would that not work the same way ¿Cómo se llama usted? does?

Hola Boros

Yes, both are correct. We use ¿Cómo te llamas tú? if we're asking informally to someone who is young or a child; we use ¿Cómo se llama usted? if we're asking formally to someone who is older or in a more formal setting like in a bank, in an interview, etc.

You can use the pronouns tú and usted or you can drop them.

Saludos

Inma