Once the parents pass away I don't think there's anything you can do but start the new generation and forcing the little ones to grow up If you kept a backup and have a copy of when the parents were alive, you could try to keep them healthy with hand gels, vitamins, fruit, enough food overnight and of course medications when necessary.

As for names, I like to switch their given name with a different one starting with the same first letter. Like if there was a little girl named Happi, I'd name her Heather or Hilary or something Good luck!