A lost, stolen, mutilated, destroyed, or ineligible Green Card or Legal Permanent Resident Card can be replaced if you fill form I-90 which you can download from the USCIS website.
The same form can be used if you want to change your name or if your card contains incorrect information. You need to submit a copy of the original court order or a certified copy of your marriage certificate, reflecting your new name, with your application. You might also replace a card because of a change of any other biographical data; with copies of documentation to prove that new data is correct.
However, immigrants with conditional resident status are not eligible to change their name through this form.
Filling form I-90 is easy just follow USCIS instructions but keep in mind that you must pay a fee of $365 plus $85 biometric fee (if applicable).
If you are a visa applicant and you would like to update your information regarding life changes such as name, dateof birth, gender, marital status, or birth or adoption of a child, you must contact the U.S. Embassy or Consulate where you submitted your application. There, provide the required documentation with the correct information (a birth certificate, passport, marriage or divorce contract, adoption documents, death certificate or any other certificate).