Drocell, I'm hoping it's just for the duration of the event..
Pepscake, normally, no you would have to let them starve to death. HOWEVER, if you do Xespa or Xoria's Cure Quest and let them test their potion on your pet, there is a random chance it will kill your pet immediately. They do not lost their names right away, AND you'll get one of these if they die:
Curse of the Undead (1)You can use it to resurrect your pet as Undead.