As long as there is no intent to defraud, you (or your new wife[congratulations, by the way]) can use any name you want. Just my opinion, of course, but the first thing to do would be to take a copy of your marriage license to the Driver's License Bureau and get the name on her Driver's License changed. Then, go see the insurance agent, Then, go get the car title tranferred to your names, and registered in your State. You might want to consider the advantages of having the title specify "As Joint Tenants With Full Right of Survivorship". That way, if anything happens to either of you, the survivor automaticly owns the vehicle. Different States handle this different ways, so get legal advice for YOUR State.
The necessary forms for Social Security name change may be available online, or it may be necessary to visit the nearest office. don't forget to notify her employer (if any) of the name change. You should be able to visit your bank and have her name added to your account, or your name added to her account, or both, whichever you want to do.
Also, remember to make the necessary changes to any credit card accounts, savings accounts, loan accounts, etc.