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What W E Ray says is correct. As far as I can tell, though, Paizo is trying to cut down on the multiple-names stuff some to eliminate possible out-of-character confusion.
I'll also add that:
(a) Razmir has managed to fool a decent number of people into thinking he is a deity when he's actually just a reasonably-high-Level arcane caster.
(b) Various tribes in old Sarkoris worshiped some local summoner Eidolons as deities or aspects of deities.
(c) Some people / places recognize the existence of the deities as powerful Outsiders, but don't believe them to truly be gods or deserving of worship.
(d) In addition to the 'gods can have different names in different places', there's also places where the same god is worshiped under the same name but with different appearances / general representations (for example, see Abadar in the Inner Sea Region vs. Tian Xia).
Taking all of these things together, I think it'd be possible for some disconnected area to invent a fictional deity out of nowhere. I think it'd be much more likely for that fake deity to be a caster or outsider of some sort rather than just an idea, but I think it'd be possible. That having been said, it'd be somewhat tricky for the fictional god's presence to continue having a notable impact once the location got into contact with actual users of divine magic from somewhere / outsider divine servants from somewhere.