Immigration is already time consuming, that's one of the reasons why I opted to keep my maiden name.
Socially, you're free to use any name you want, unless it's to do fraudulent activities. You can introduce yourself as whatever you want/the number of people who will see your IDs is limited.
ETA: the Canadian consulate in NYC would know if they can update your passport to the name(s) on your marriage certificate. That's another place to inquire/they are aware of how things are done locally. Not a perfect solution, but seems easier than the birth certificate change.