Does Fiora's Sword have a name?

if it does, then here's my question; does it still have a name when it's a ruler or a noodle, because that would be hilarious

No her weapons are just described by what they are,Bluesteel rapier in classic and Zero pulse blade in her Project skin I think

Amusingly, in the Jax lore it's mentioned that Fiora uses a saber. Despite her own lore poking fun at her opponent for using a saber in their duel.

This is amusing since Fiora's weapon is clearly not a saber, unless you count things like the Patton Saber, which you shouldn't unless you consider a dung beetle actual dung. And sabers are fine dueling weapons. I'd personally prefer the reach of a rapier, sure, but saber's were used in duels as well and a good practitioner could hold their own.

But as to the actual question, no, her sword was never given an official name.