"My name" said two ways

I have just started learning Spanish and have been told that 'mi nombre' and 'me llamo' both mean 'my name is....' Can you explain why one is used versus the other in a conversation? Is one more common to Spain and the other more common to Latin America? No one seems to be able to explain this adequately.

Me llamo comes from the verb "llamar" and is used as a reflexive requiring a complementing reflexive pronoun. It is translated to: I call myself. llamo is the "I call" and me is the reflexive pronoun for "myself". In my opinion me llamo Patrice is the most common response to: ¿Cómo se llama? or when wanting to introduce yourself to new friends, etc. "Nombre" is used as a noun. In my opinion mi nombre es Patrice is a more common response to ¿Cuál es su nombre? I think this is more when registering in a hotel for example or some place where they want your complete name. I don't believe it is a regional thing, but let's wait and see if anyone else chimes in to help explain.

Personally I like to say 'mi nombre es' just because I think it sounds better. But that's just an opinion. 'Me nombre es' means 'my name is'.

"Mi nombre es Dan" translates logically to the english-oriented ear. But it seems, in my limited opinion, that "Me llamo Dan" is the more widely-used phrase. I will be interested to see where the more experienced Spanish speakers land. I may also discuss this with my Spanish tutor next week to see which is most common in her country.