If your end goal is to live together in the US, then it will not have an affect on the process. If you were to move to El Salvador, it is recommended to register your marriage and your daughter's birth* at the Seattle consulate.
*You can register her birth even if your goal is to live in the US. She is eligible for dual citizenship because of Salvadoran law. After registration, she will be eligible for a Salvadoran passport; thus no need to pay the $10 tourist fee to enter CA-4 area (El Salvador, Guatemala, Honduras, and Nicaragua) and, as of now, visa-free travel to Brazil, Paraguay, Russia, Turkey and visa on arrival in Iran: https://www.passportindex.org/comparebyPassport.php?p1=us&p2=sv&fl=&s=yes
Women in this country are not required to change their last name upon marriage. It’s a personal choice. It will make no difference - you have the right to keep your maiden name.
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