If my husband getsthedivorce in Canada, do I have to also get it in the state in which I live?

If you are both still living in the United States, the divorce should be entered here. However, if he is now living in Canada, he can file for divorce there. Generally, divorces granted in other countries are recognized in the U.S. based on comity, provided that the procedures used were adequate (i.e. proper notice). 

The Uniform Act on Marriage and Divorce (1970, 1973), 9A Unif. Laws. Ann. 461 (Supp. 1965) is in force in Arizona, Colorado, Georgia, Illinois, Kentucky, Minnesota, Montana, and Washington State. Section 314(c) of the Uniform Act on Marriage and Divorce establishes a procedure for the clerk of court where the divorce decree is issued to register the decree in the place where the marriage itself was originally registered. The Uniform Divorce Recognition Act, 9 Unif. Laws Ann. 644 (1979), specifically denies recognition to a divorce decree obtained in another jurisdiction when both spouses were domiciled in the home state. The Uniform Divorce Recognition Act is in force in California, Nebraska, New Hampshire, North Dakota, Rhode Island, South Carolina and Wisconsin.

Obtain a certified copy of the foreign divorce decree from the court in the foreign country where the divorce decree was issued. 

Once the divorce has been finalized, you can go to the Social Security Administration to have your name changed. It does not happen automatically. Be sure to bring a copy of the divorce decree with you.

I would recommend that you contact a divorce attorney in the state where you currently reside. Best of luck to you!

The U.S. Department of State's website is a very useful source for your situation: http://travel.state.gov/law/family_issues/divorce/divorce_592.html

If your husband lived in the Uniited States, he would need to file here most likely. If he is still a resident of Canada and has obtained residency there, then you need to speak with a divorce attorney about conflicts of laws and who has the better jurisdiction for you in order to ensure you get the most assets out of this marriage or at least the fairest separation of assets. Further, your name does not automatically change. In any way, once your divorce is final, all you have to do is go to the Social Security Administration and change your name, then use your new Social Security Card to change your drivers license and any other state issued IDs.