This takes place in Realms. When we go to name a name tag it does not let us. We put the name tag in the anvil, type the new name, and then it still only gives an 'X'. It is not an issue of too many characters or not having enough levels. 
Is there a limit to how many mobs can be named? We have named a large number of mobs lately. (Many of the mobs de-spawn even though we have named them but that's another issue, I guess).