*SPOILER* So I think the new primal in 3.5 part 2 is...

[ArcaviusGreyashe]

To be fair, we already had a manifestation of the twelves... Right before Louisoix became Phoenix (2 years old spoiler is not a spoiler) the scions and the people of Eorzea were praying, hence the symbols of the twelves appearing around Bahamut. And in a text that was published to commemoratevthe first anniversary of ARR, I think, Louisoix explained to Minfillia that doing that required the same energy as summoning a dozen primals...

Plus, we don't even have to have this conversation, because it's ever clearer that a primal is just what its summoners want it to be, or figure it will be, hence Enkidu, hence Titan grieving for the death of a kobold child whose sorrow was more important than the other kobolds' hate... The twelves may have existed (although I do believe that the only gods that exist are Hydaelyn, Zodiark and Midgardsormr, all the others are just glorified primals-, but a primal is never a god. As I said, it won't be Rhalgr himself, but it will represent Rhalgr.

[Hinoto-no-Ryuji]

As I said, it won't be Rhalgr himself, but it will represent Rhalgr.

Unless, of course, the Twelve aren't based on prior, actually-existing beings, and instead are thought-forms of culturally-significant values and beliefs; if Rhalgr didn't/doesn't actually exist, any Primal manifestation will be Rhalgr himself, as there's no "original" for it to represent.

[Torquil]

if Rhalgr didn't/doesn't actually exist, any Primal manifestation will be Rhalgr himself, as there's no "original" for it to represent.

If no true Rhalgr actually exists, no manifestation will be Rhalgr as there is no Rhalgr to BE. The summoned entity is itself, but is not a "true" Rhalgr (since the premise is none exists).