Whenever rare or legendary items drop, they have generic item names like "Sheath" or "Heaven Hand". Is there any way to tell what the base item is after the item is identified?
Using the Official Diablo 3 Game Guide's Item Guide you can easily work out what your weapon's base name is just based on it's picture and item level (and use level for lower level items that don't show an item level).
For example: lets say you have a level 60 fist weapon with an item level of 63, all you need to do is go to the guide, and under Weapons > One Handed click "Fist Weapons (Monk)", then scroll through the items and you'll see that on page 2, there's a Fist Weapon called Heaven Hand that is item level 63 fist weapon. If you happen to own an ilevel 63 fist weapon, you'll also note that it has the same picture. Therefore, you can conclude that your ilevel 63 Fist Weapon's base name is "Heaven Hand".
This same reverse engineering can be done with any weapon or armour piece. Of note is the fact that all Legendary and set items have their actual name instead of any sort of base name, this is due to the fact that legendary and set items inherit the base name of a weapon/armour piece of the same type, normally of the same ilevel, but sometimes an ilevel up or down.