How long does it take to change your last name on your birth certificate?

My husbands name for example is Richard Smith-Allen, but he wants to drop the Smith and just have his name be Richard Allen. How long will this take? Also, it's a little complicated, because he's living in Canada on a student visa, but he is an American citizen, so would he need to do this process in Canada? Or will he have to do it in the US? How long will it take? BTW, I would first need to sponsor him so he can have permanat residency here and eventually become Canadian citizen. So, anyone that can give his some direction from here would be greatly appreciated.