Correct. Palladia-Mors references itself by name, which really only means [this object]. So even though the object was not named Palladia-Mors when it dealt damage, it has that name now and thus the ability to grant hexproof is not active.
What happenes if Palladia-Mors, the Ruiner deals damage to something, but that damage is prevented?
(I'm assuming it sill keep hexproof as technically it didn't deal damage)
Damage that has been prevented wasn't dealt. Therefore if all the damage has been prevented, Palladia-Mors did not deal any damage yet this turn. So the phrase "deals damage to something, but that damage is prevented" is non-sensical as it is a contradiction in itself. The damage was either dealt or prevented, not both.