¿Me llamo José o Yo me llamo José?

Is this difference really that important? The answer is no and yes (respectively). Saying Me llamo... or Yo me llamo... depends on the situation.

I won't give you a rule yet, take a look at these situations and get the rule for yourself:

1st situation:

One guy and one girl are introduced by somebody else:

He: ¿cómo te llamas?
She: Lola, y ¿tú?
He: Yo, Migue. Encantado.
She: igualmente.

But wait, they didn't even need to say me llamo nor yo me llamo. So, does the rule say you don't have to use these formulas to say your name? Well, first of all, most Spanish speakers don't say me llamo or yo me llamo when they're asked their names, so either you say me llamo ... because you learned it in some Spanish lesson, or you say this, which is easier and, as a matter of fact, more common.
Anyway, you have to hear and understand what you're being asked, your name, so that means you went to class and were a good pupil. Problem solved.

2nd situation:

You want to write an ad on the internet to look for somebody to practice Spanish with you online. Nobody's asking you this time, so to introduce yourself, we know for sure you can't just say: José.

Hola, me llamo José, soy de Málaga y tengo 29 años. No quiero practicar español con nadie porque soy nativo, pero es un ejemplo del uso de "Me llamo". Hasta luego, ¡chao!

3rd situation:

So far, so good... But you're wondering: what's the difference with yo me llamo...? Could I say it here? I'll give you another context...

The students of a class of Spanish are introducing the first day. Pay attention:

- Yo me llamo Alice y yo soy estadounidensa.
- Yo me llamo Frank y yo soy canadienso.
- Yo me llamo Marie y soy francesa, de París.
- Yo me llamo Joseph y yo soy ingleso.

Quite good! Except for some small mistakes... Do you see them? Yeah, estadounidensE, canadiensE and ingléS.

But the point is: why did they say (excellently and with its appropriate context) yo me llamo... even though they made some other mistakes? Because there's more people giving the exact same information (name), and thus, this yo gives us the individuality of my name in opposition to the others names.

Well, they probably didn't know that, because their languages force them to always say Yo... Moreover, there's still one not so obvious mistake that tells us that their languages force them to say so: they put a second yo: YO me llamo Alice y YO soy estadounidensa. Since she started with one YO, there's no need to repeat it. Only Marie introduced herself with no mistakes.

Well, this was just the first tip to keep in mind for those who want to speak correctly: small words sometimes make a big difference.

¡Hasta la próxima!