As mentioned in the “How do I need to enter my name on Form I-90?” article, you must enter your full legal name into the fields 3.a to 3.c in Part 1 on Form I-90. But if your name was changed since the time you acquired your current green card, you must also fill out the fields 5.a to 5.c. in Part 1.
If you changed your name, enter your current name in the field 3.a to 3.c. After that, you must check the box “Yes” under the item 4 “Has your name legally changed since the issuance of your Permanent Resident Card?” Then, write your old name as it was printed on your green card in the fields 5.a to 5.c on the form. Note that the first, last, and middle names must be exactly the same as on the card. Remember to provide a copy of documents such as a court order, marriage certificate, or similar documents to prove that your name was legally changed.