The Conan stories take place on prehistorical Earth, before the last Ice Age.

Yeah I agree and didn't know the Stygians were connected with Egyptians - always assumed the Conan stories were taking place in a fictional world (not a fantasy-like Earth).
Ram-Amon? Didn't he have a very pharaoh-ish appearance; wearing a snake-motifed, Egyptian-like "crown" and have one of those chin-ornaments (also resembling a cobra)? This character is from the cartoon - which I am a fan of, and prefer to this movie (not the original) and the remake. Making a film or a trilogy of movies based on that Conan: the Adventurer cartoon would've been awesome to see

It would be nice to think that there would be some higher intention to the use of the -Amon suffix, but frankly, I think it's just because of association with snakes/Set combined with association to the original - Thoth-Amon.
Thoth-Amon appeared in "The Phoenix on the Sword," and was referred to in "The God in the Bowl," "The Hour of the Dragon" and the non-Conan story "The Haunter of the Ring." The name seems simply to be a conjunction of the Egyptian gods Thoth and Amon (usually spelled Amun, though Amon is accepted): Thoth-Amon is a Stygian, who were the Hyborian Age ancestors of the people who would become the Egyptians.
Thoth-Amon was boosted into Conan's nemesis by subsequent authors, and made his mortal foe in the comics. Because of Thoth-Amon's presence, his role as a Set-worshipping sorcerer and the suffix -Amon was repeated in different continuities:
Conan the Destroyer
as Toth-Amon, and
Conan the Adventurer
as Wrath-Amon and Ram-Amon.
Since the stories, films and cartoon all occupy pretty much incompatible universes, it's very unlikely Thoth-Amon exists in
Conan the Adventurer
, or Wrath-Amon in the comics.