Well Bahamut is frequently referred to as the Dreadwyrm. It makes sense to name gear and an action behind a title of the Dreadwyrm, Bahamut (it also rolls off the tongue better and sounds cooler). When it comes to achievements, I feel all teams are given free reigns (especially with quest and FATE names, as names of FATES, Quests and Achievements do not affect the story/world in any way).

English: In For Garuda Awakening | Japanese: 'True Arashi God of Goda' (I'm guessing True wind God, Garuda?) | German: 'Gods Dawn - Garuda' | French: 'A Wind Of Panic'