To go into the specific names, from what I remember:

Ifrit - Tempered (also blanket name for the condition)
Ramuh - Touched (So far, only Sylphs have been tempered by him)
Leviathan - Drowned (I think only the Spoken races have been tempered; the Sahagan quests imply they are not tempered at all)

Garuda - Unknown (even though the Ixal are tempered, and she tries to temper the WoL, I can't remember it ever being named)
Shiva - Unknown (don't know if she even Tempered anyone)
Good King Moggle Mog XII - Unknown
Thordan - Unknown (possibly Blessed, like Dualblade said)
Bahamut - Unknown (think they just use "tempered" or "enthralled" in Coil)
Alexander - Unknown (even though it hasn't been outright stated, its highly likely the Iluminati are tempered)


As for Titan, Ravana and Bismark...their followers don't seem to be tempered, and we don't have any instances of them tempering anyone (in 2.0 for Titan; yes, it was mentioned somewhere that the Company of Heroes had to fight their companions after being tempered, but I don't think anything specific was mentioned about it)

Phoenix and Enkidu weren't really able to Temper anyone (headcannon: Gilgamesh has the Echo when in Eorzea), so...

And Odin is Odin.

EDIT: Forgot the Triad. All Unknown lol