The problem of American green card citizens

No problem. With the consent of his citizens, he can use his real name as his former name when applying for a passport. As long as you go to the local authorities to notarize your relatives and prove that you and the person with this name are father and son, you can apply for a green card.

Now that your father has got a green card, it means that his illegal residence has been exempted by the US Immigration Service, and there will be no trouble in the future. Immigration officers mainly look at the applicant's current status.

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My cousin sneaked into the United States that year, and later got a green card and applied to become an American citizen. Now he has applied for his wife and parents (my uncle and aunt) to immigrate to the United States, and there is no problem at all. What you need to solve is the proof of your kinship with your father, which is handled by the relevant foreign-related notary office in China, and has nothing to do with the US Immigration Service. Your father only needs to change his name here after naturalization. Pay a lawyer's fee and sign it. It's a simple thing.