Ethically you can't change a thing. Do a new one.
Any change, however slight, completely invalidates it. You have to realize that some of the signers may be dead, have changed their mind about the issue, or don't want to address the new governor in that way.
It would completely undermine the credibility of the persons or organization submitting the "new" petition, and hurt the overall cause, if you were to just "change the names and dates" and re-submit it. It's kind of like submitting a copy of a note from Mom six times in a row when you're late or absent.
Besides, politicos live and die on the most current polls and information - smart ones wouldn't even give a stale petition a second glance before tossing it in the trash, and with good reason: they want the most recent, valid information in order to set their policy.
Do a new one - it'll have credibility and more of an impact.