Phrases in Spanish to talk about names?

There are a few ways to talk about a person's name in Spanish, whether it is yours or someone else's.

The most common way to introduce yourself is to say, "Me llamo (Insert Name Here.)" You could also say "Mi nombre es (Insert Name Here)."

To talk about someone else's name, it's very similar. To say "His name is Jose," you could say "Se llama Jose" or "Su nombre es Jose." It is the same for male and female names.

If, for some reason, you needed to tell someone that their name is María (amnesia, perhaps!), the correct translation would be "Te llamas María" or "Tu nombre es María." Recall that the use of te llamas/tu should be used only for individuals with whom you are familiar and/or friendly; in all other cases, it's generally more prudent to use 'usted' - "Se llama María" or "Su nombre es María." (Though why you would be telling a stranger their name, I can't imagine.)

Finally, to ask someone their name, you should ask "¿Como te llamas (tu)?" (informal and familiar) or "¿Como se llama (usted)?" (formal in order to be respectful of those you don't know at all or that are older). You can also ask "¿Cuál es tu/su nombre?"