Let me explain. The Dragon King is not a character, it is a status, an energy force that is bestowed upon someone. That's why The Dragon King has no name as of yet.

The boss of MKD is Reptile the Dragon King. So now Reptile IS the Dragon King, he isn't possessed by the spirit of the Dragon King but has been bestowed with new powers, a new form and a new purpose (to rule all realms yadda yadda yadda).

If Liu Kang happened to be where Reptile was when the Dragon egg hatched, then Liu Kang would become the Dragon King and be bestowed with a new form, new powers and a new purpose. Thus his name would now be Liu Kang the Dragon King.

Think of this is a virus, it infects one person and that person gains new characteristics, when that person dies the virus either dies with him/her or goes dormant until someone else is infected.

The Dragon King has no name because there have been MANY Dragon Kings with different names.

So the name of this new Dragon King is Reptile.

Just a little theory I had.