You don't "apply" for a name change unless you're legally changing your name just out of the blue. If however you've recently been married and are assuming your spouse's name, all you need to do is go to the appropriate offices and show them your marriage certificate and fill out the name change form.
A legal name change requires a court appearance IIRC.
Most of the offices where you would need to change your name (SIN, provincial healthcare, driver's license etc etc) have forms on their websites to download, then you can mail them in if you're not in Canada right now.
Do you currently have a passport? Or have you never had one and you're in the US and find you can't leave now without one due to the June 1st law that will require passports for everyone?
You can apply from the US for your passport, without having ot wait on everything else.
http://www.ppt.gc.ca/cdn/form.aspx?lang=eng®ion=USA You'll need to send them your birthcertificate, as well as your marriage certificate. They'll send them back. You can probably get extra copies of your marriage certificate from the county offices in the county where you were married.
Go to a Sears Portrait Studio to have your photos done. Most other US passport photo places can't/won't do Canadian passport photos. Sears did mine last month, and they knew exactly what they were doing, and the photos were accepted first try.