Should I apply for my green card or my citizenship after legal name change?

You do not have to correct your name on the green card before applying for your US citizenship. I note that USCIS does requires individuals to have green cards with at least six months validity on them when applying for citizenship. That is usually the only time that individuals must apply for new green cards when applying for citizenship. As you already have a legal name change, you can enclose a photocopy of the court document changing your name in your naturalization application. To lessen confusion in any day-to-day situation, you can carry a copy of your name change document with you along with your green card or a copy of it. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.