Adding surname/Lastname in Passport after H4 Visa Stamping

Hi,

My wife has H4 stamped and it is valid till Jan 2019. Currently she is in India and will be travelling to US in Feb 2017(on H4 Visa). She doesn’t have Last name in passport and her name in the visa is printed as FNU Swathi Puttur Krishna. Now, I would like to reapply new passport for adding surname(last name) and want to put “Puttur” in the surname (taking middle word from current given name). So the final name in the passport is:

Given Name: Swathi Krishna

Lastname/surname: Puttur

Questions is:

“Once we get the new passport (with the last name in the passport), do we need re-stamping with the updated name on the visa” Can she enter US with the old name on the visa?

Keep a good color photocopy of the current passport(all pages) with the visa.

Apply for the passport correction(its a correction not name change).

While applying, if you need to submit the current passport, include a letter to return the current passport as it is since you had a valid visa stamped in it.

Once you get the updated passport, keep the old and new passport together and keep using the new passport. If anyone asked about the visa, show the visa in the old passport.

keep a copy of the issue fix application, request etc…