Not sure if it is exactly the same thing. My wife chose to take my family name when we married. Additionally, she adopted her Russian patronymic name as her middle name even though Russians do not have what we consider a traditional middle name, and we did all of her immigration documents with that format. All of her U.S. based ID’s, DL, GC and now U.S. passport reflect that new name, but her Russian documents are still in her name at the time we married. Changing her name on those documents is a bureaucratic fuss, so she has left it as is, and she has had no issues when traveling back to Russia. She carries both passports, or previous to her naturalizing, her Russian passport and U.S. GC, along with a copy of our marriage certificate, and has had no issues so far. Over 11 years, no one has actually questioned anything, or required her to show the marriage certificate.