Many states grant a legal name change when the Foreign National spouse gets married—this new married name is usually printed on the marriage certificate if you apply for the license requesting the name change. If the new name is printed on the marriage certificate, it gives the Foreign National the right to elect to use their spouse’s last name or to hyphenate their name with their spouses name. Whatever decision is made at this point, the Foreign National should going forward, consistently use the name they opt to take. 

“I just got engaged to my fiancé and we are anxious to begin our American Dream Life together. We’re ready to get married but are not sure if it’s better to apply for fiancé visa now or get married and then apply for a marriage visa. What should we do?”

Entering as a boyfriend/girlfriend on the visitor visa, or ESTA (also known as the Visa Waiver Program), is not in and of itself a visa violation. It can, however, become a problem if the girlfriend/boyfriend plans to use the non-immigrant visa to enter, and then take actions that are contrary to the intent of the visa by, for example, getting married to their US citizen love interest. This is because marriage to a US citizen implies immigrant intent, according to the US immigration laws, and traveling with what's called "dual intent" is strictly forbidden when it comes to the visitors visa or ESTA.