Permanent Residency Green card through marriage

[GPS_]

I am a Canadian Citizen, married to an American, I got my Green card today and it has my previous married name on it. I assume it is because I didn't have enough time to get a new Canadian passport before my interview with the correct name. Do I need to change the Green card to my new married name, or just leave it until my card expires?

 

[Michael Wechsler]

You probably want to change your name and that can be done here:

Application to Replace Permanent Resident Card

This should have all the information you need about filing, including the form which is for:

"Your name or other biographic information has changed since the card was issued"