You can't reforge your ring to change a particular characteristic.
You can however speak to Zouti Fizzlefury at Zagarra to buy the other ring available to your class which will have two preset different secondary characteristic, which might be more to your liking or simply be a better choice for your second spec.
- Intellect ring: Versatility & Mastery or Haste & Spirit
- Strength ring: Critical Strike & Multistrike or Versatility & Bonus Armor
- Agility ring: Critical Strike & Versatility or Versatility & Bonus Armor
Typically the first one is for dps and the second one for heal or tank.
Note that the second ring won't be upgraded during the legendary quest line, so you'll have to rebuy it at each step if you don't want to wait the final step to buy it.
- ilvl 640: 500po
- ilvl 680: 1000po
- ilvl 690: 1500po
- ilvl 715: 2000po