You can respond with:
* "Me llamo..." (My name is...) and then say your name.
* "Mi nombre es..." (My name is...) and then say your name.
For example:
* "Me llamo Juan." (My name is Juan.)
* "Mi nombre es Maria." (My name is Maria.)
You can also ask the person their name in return:
* "¿Y usted?" (And you?)
* "¿Y cómo te llamas?" (And what is your name?)