Name change on Passport with valid US Visa

Ma name has 3 sections xxx-yyy-zzz. In the passport all 3 have been written on the given name field and surname field is empty. Also, in all my other documents, my name is in the order of xxx-zzz-yyy. So I have to interchange my middle and last name, and also, get my surname and given name fields filled correctly in the passport. I currently have a US tourist visa stamped with the same xxx-yyy-zzz and FNU. As i want to give GRE, TOEFL exams, this is going to be an issue. So I have to get a re-issued passport with the name change. But how will I make the changes in my current US Visa? Will they stamp a new one and update my name on their system? Who do I contact to enquire about the US visa?

Unless its a major name change you are good, what i mean is splitting the name.

Even i dont have a surname in my passport, but you can always split the name in the passport and carry the old passport with VISA, i am not entirely sure if you have to go for stamping again.

Check this article Surname Blank Issue Passport FNU US Visa on the process to get it corrected.