I'm not 100% sure, but the site I have used to plug in my info, only requires a last name and correct mailing address.
https://disneyworld.disney.go.com/pin-enter/
Once you enter just your PIN, last name, and zip code, your offer gets "looked up". Then on the next screen, you are asked to verify your last name and complete mailing address. I honestly do not know how the first name on the mailer factors into it.