If you normally live in the USA and were married overseas, you can still change names following much the same process as everyone else. Always start by changing names on your social security card. The SSA accepts foreign issued marriage certificates as evidence of your marriage and name change.
Once you have an updated SSA card you can apply to change names on your photo ID. Most state DMV's require you to visit in person so your photo can be taken, signature witnessed and they can check your original identification. States have varying laws as to what documents will be accepted, so there's no one rule for everyone. We always recommend checking the DMV website or calling in advance to check your foreign marriage certificate will be accepted. Often you can show a number of other original proof of identity documents, so if you don't have enough, consider getting your passport or bank and utility records changed into your new name first.
Ultimately it's each agency's call on what documents they need. If you don't have the right documents your request may be rejected. Some may insist on a legal name change from the court. There's almost always a way around this. Always start with federal identification, update records in as many other places, then use all this new evidence to support your request for changing names.