You'd have to use damage values on a specific item. It's hard to explain but there are tutorials out there. However, my conquest texturepack has the codelines in the diamond_sword.json file.

If you want a specific name, you'd have to enter the file, preferably using notepad ++, press ctrl + h and replace the texture name to the custom json file of your diamond sword. It's really hard but do able :)

Goodluck!