Dear igvelesiani
I just spoke with a good friend of mine who is an immigration attorney - (and a good one only lost one case in 27 years) This is what he told me
To change your last name based on marriage, no formal name-change procedure is required (via the court). Just take certified copies of your marriage certificate to the various authorities (Social Security, Motor Vehicles, etc) and apply for a new ID. Changing your green card is just a matter of filing Form I-90 (note, if you are a Conditional Resident based on marriage, don't apply to change your name until the conditions have been removed).
If my answer has been helpful, please ACCEPT. If I can be of further help, let me know. Appropriate FEEDBACK is appreciated as is a bonus. Thanks ~ Michelle