Also, my son's birth certificate states my maiden name, do I need to change that to reflect my new name? I was already married when he was born, but registered him under my mainde name as all documents stated that name.
When you travel, take paperwork that shows your name transition. but make sure you have good copies kept very safe at home. If you are close to naturalization, spending 9 months getting a new green card may not make much sense. If your green card is based on marriage, your choice of naming your son is strange. And you might want to deal with that sooner rather than later particularly if you have conditional residence.
What you should do is apply for a new green card with your new married name. If you insist on traveling before obtaining that, then make sure to have all the necessary (original) documents with you upon your return to be able to prove that the two last names are in fact one person and that it's you.
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Yes you will have no problem though you should file I90 to change the same unless you are soon due for N400 and would do that at that point.
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