Tu t'appelles comment?[:

What is your name?

or
What do you call yourself?

Thank you,[: And the correct response would be, Je m'appelle *NAME HERE*..?

Right!

Better word order for French is:

Comment t'appelles-tu?

Sra (aka Mme)

P.S. The most common way to ask a question in French when using an Interrogative (Qui, Comment, Combien, etc.) is:
(Example above) Interrogative word first and then inversion

Je m'appelle Explain Bot.