I agree. I wouldn't have a problem with them coming up with a new name, but it seems suspiciously set in stone. Perhaps the name has been a classic for too long? That's honestly what I think. Everybody knows "Lightning Tiger Blade", or "LTC".
One of my pet peeves are the Greek letters! They need to stop. Like Sword Rain: Alpha and Beta, Omega and Psi Tempest, or—speaking of Lightning Tiger Blade—Tiger Blade Sigma. I would like an overhaul on those arte names, specifically. (I'd be fine with "omega" were it referring to a "finality" aspect of an attack, but it doesn't look like it's doing so with Sword Rain: Omega or Omega Tempest.) I'm with the idea of renaming all Sword Rain artes to season- or weather-themed attacks, where necessary.
My YouTube and MediaFire files—be anyone interested.