I've seen many duplicate first or last names on my server. But I would imagine there would be a conflict if more than one person had the same first and last name. Not to mention it would be annoying with a hundred people named "Cloud Strife" running around.

In FFXI you had to change your name upon login after changing servers if that name was already in use on that server. I would guess a similar system would be in place in FFXIV.