Help! Different names on publications and passport

I have an issue here. The spelling of my passport name is different from the spelling I use in all of my publications. Would that be a problem for my case? Which name will be used for my green card?

Can you correct the spelling of your passport name to match your papers? I think you may consider doing so since it's difficult to change your name on all the papers you have published....

to sally.nichols383:

I don't need it's that simple to just change your name on your passport....Do you have a lawyer for your case? I'd talk to her/him. There might be another way to show that you're the same person. Some statements/letters of same name? something like that