It appears that there is more than one naming convention for magic weapon naming when one weapon can take a variety of forms:

1. To put the generic form, then a comma, then the specific. E.g.: a scimitar with the properties of the Blade of the Medusa or Gambler’s Blade would be a Blade of the Medusa, Scimitar or Gambler’s Blade, Scimitar, respectively.
2. To replace the generic weapon type with the specific. E.g.: a scimitar with the properties of a Weapon of Warning or Vicious Weapon would be a Scimitar of Warning or Vicious Scimitar, respectively.
3. To add the weapon type immediately after the generic name, as with the Dragon Slayer and Dragon Slayer Scimitar.
4. To add the weapon type in parentheses, as with the Armblade and Armblade (Scimitar).

The Moon-Touched Sword varieties seem to follow the first convention (e.g.: Moon-Touched Sword, Scimitar), but the version specifically for the rapier is missing the word "Sword" in the name (Moon-Touched, Rapier), and appears to be the only one of the Moon-Touched Swords affected by this.

Unrelated to the above issue of the missing word, and only my personal opinion, but the second naming convention above feels better for the Moon-Touched Sword.

Edit: Added the fourth naming convention.