At present, only DK's Frostmourne has a special name. DH's war turbine and so on, as we say, the sword and gun ... are just the classified names of weapons. There is no special mention of the weapons they use in the background story of Warcraft.
If you have to pursue it, just play WOW:
DH uses two Essinos blades.
The snake ridge longbow used by Naga banshee Vaqi.
The lich Kel 'Thuzad used "Etiyesh", a defiled legendary scepter.