Is there a way I could change my promo code to something else?

Yes you can, but you have to message or call Rover support and have them change it. I've done this in the past. I don't think they liked it, but they did it. :) You can call [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team] or message them through the site at https://support.rover.com/hc/en-us/re.... Remember that if you have business cards, the promo code on the cards probably won't work anymore.
Edit: Rover's posted answer to this question is "Your promo code and URL are permanent. That way, if you’ve already shared the code, it won’t suddenly stop working for somebody trying to redeem it later." (See the very bottom of https://support.rover.com/hc/en-us/ar...)
Still, it can't hurt to ask, and the answer may just depend on who you get on the other end of your email/phone call. I'm glad they did it for me. I hope they can do it for you, too!