Words are masculine or feminine in French.
To say 'what is your name', we say 'how do you call yourself'. We can say "quel est ton nom?" but it is more common to use the verb appeler.
Pay attention to "nom", it is for lastname. Nom also means 'noun'.
So name should be for prénom.
There are many ways to say the same thing in French: c'est quoi ton prénom?, ton prénom c'est quoi?
Un petit nom is not a nickname, it is first name.