Idioms -
To give one's name:

English: My name is Ana.
(page down) Me llamo Ana.
The literal translation is "I call myself Ana

English: Their names are María and Jaime.
(page down) Se llaman María y Jaime.
The literal translation is "They call themselves Maria and Jaime."

In giving one's name, the reflexive construction is used. Although it is possible to say "His name is Juan" ("su nombre es Juan" - refer to Possessives for possessive adjectives), the more common expression is "He calls himself Juan," or "I call myself Ana," etc.
Likewise, to ask "what is your name," you ask "how do you call yourself" ("¿Cómo se llama usted?

The correct grammar involves the reflexive object pronoun (this is another function of the object pronouns) and a simple conjugation of the verb, "to call" - "llamar." This pronoun is translated "myself," "yourself," "himself," "herself," "ourselves" "yourselves," and "themselves" and must be used with this construction. The reflexive pronoun is always used, even if the subject is another noun:
"What is the profesor's name?" - "¿Cómo se llama el profesor?" ("How does the professor call himself?")

Spanish:
me llamo…
te llamas…
se llama…
nos llamamos…
os llamais…
se llaman…

English:
My name is … (I call myself)…
Your (singular) name is… (you call yourself)
His, her name is… (he, she, calls him/herself)
Our names are… (we call ourselves…)
Your (plural) names are…(you call yourselves)
Their names are… (they call themselves)