FF has a long tradition of naming weapons after famous historical weapons. Joyeuse was the sword of Charlemagne, Ridill the sword of Regin the younger brother of fafnir.
The tradition continues in xiv with the some of the relics.

Curtana- The sword of Edward the Confessor, king of England. It is the sword carried before the english monarch, symbolically broken at the point to symbolise mercy. Itself Named after Cortain the sword of Roland, chief paladin of Charlemagne.

Gae Bolg- The spear made from the bones of a sea monster and weilded by Chuculain in irish mythology. It's name means spear of mortal death or belly spear.

Sphairai- Not a famous weapon this time. Sphairai were the padded leather thongs wrapped round the knuckles by boxers in ancient greece.

Artemis bow - Artemis was twin sister to Apollo. A goddess known mainly as a huntress with a golden bow and arrows. In xiv the relic bow has a harp or lyre built into it. The Lyre was invented by hermes for Apollo (god of music and poetry). It seems fitting that both these twin gods are represented in the bards weapon.

Thyrus - In xi this is usually considered to be named for Thyrsus the staff carried by Dionysus. It was made of fennelwood and wreathed in Ivy.

I dunno about the derivation of the names of the other two.
Anyone know what any other stuff in xiv is named after?