O16 said:

Considering that exist "complete" dictionaries for formal and informal english for each english-speaking country and many knowledge sub-fields have their own dictionaries as well; that encompasses almost every word except for the non-popular neologisms.

Then you have answered your own question.

I mean, we're talking about names here. If your name is a single word it's probably not unique, if you use two random words chances are your name is now already much more unique. The border where an amalgamation of common words becomes unique is fluid and depends on a bunch of factors.