It sometimes can vary between FF titles as well, Fire, Fire 2 and Fire 3 were naming conventions of FF7 as an example. And Fire, Fira and Firaga can also be upgrades of each other in FF titles.

But I like how XI handled the differences and maybe this would probably fit a little better here too. Fire denoted your single target Fire element spell, whereas Firaga was your AoE version. As different types of "Fire" spells ended up being added, they also got Firaja and Fira. So Fire, II, III etc existed there as well as Firaga, II etc also existed. I can see how, although a subtle change, it'd be nicer to have names to indicate variation in use and be a shoutout to FF naming conventions. Fire II might be better served as a Firaga to indicate it's an AoE and Thunder II/IV could be Thundaga I/II. Blizzard 2 would be Blizzaga. A part of me would probably want to rename Freeze to Blizzaga II in light of its change in functionality. Though Freeze is still a FF naming convention.

By extention it could work for WHM too.