What to do if I'm on my OPT and my employer sponsored me for green card but I noticed that in my current passport my first name and last name are in the wrong sequence?

Question Details: My first name appears as the last name and my last name appears as the first name. My birth certificate has the correct first and last name sequence but the passport shows the wrong sequence. So to avoid any problems in my green card my attorney asked me to change my all the US documents as per to my birth certificate. but when i contact local US Embassy to change my name on my visa they asked me to come in person and submit new visa application which is impossible in my situation. Can you please advise me on this whether do I really need to change all my US documents?

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