When I get my divorce, should I notify credit card companies?

You should notify all credit reporting agencies and credit card companies about your new, unmarried status.
You should notify the credit bureaus of both your and your ex-spouse's new names and social security numbers, addresses and specify that those accounts need to be reported separately.
If you do not, transactions may be reported on the wrong spouse's account. This will help limit your liability and make you resposible for only your future obligations.