My mother has a 10 year multiple entry B2 visa stamped in her passport issued in 2006. Currently she has no last name on her passport, so on her visa, her First Name is written as the Last Name and in place of First Name, it says FNU. I will be eligible to become a citizen in March next year (2012), and want to apply for her green card right after. We have had trouble with her FNU situation, and now I would like her to officically change her name to include my father's last name and as a result get a new passport. I have read the forums to find out that she would still be able to travel to the US using her existing B2 visa stamped on her old passport, but not sure. My dilemma is to whether to change her name now in India and risk her losing the B2 visa and denied entry to the US, because she has changed the name, or apply for her green card and later change her name in the US. If any of you have been in a similar situation, your input will be appreciated.