You can change the last name after marriage when showing social security department the marriage certificate. Doubt if you can change your first name. In DMV, you can change the name on ID but need to show official paper of the new name, for which you have to go through the first step. Besides DMV has no responsibility to let others know your name change.
If you want to have trouble free process, court is the formal way and it costs around $50.
If you want to have trouble free process, court is the formal way and it costs around $50.