Which FC name sounds better?

[Kitya]

I agree.

Crystal Company seems a bit redundant. It's like naming a guild (in a different game) Crystal Guild.

Crystal Covenant sounds way too serious. Yes, "Covenant" works for Halo, but it doesn't really fit with Final Fantasy.

Crystal Alliance works in so many ways, especially with the story.

I agree with your point but disagree with your choice. Say Crystal Alliance out loud. the "al" twice in a row makes it feel kind of clunky.