Parents name mismatch between B1/B2 visa(issued on old passport) and recently received new passport

[ssjgoku]

My parents are planning to make a trip to visit me. They have previously visited me and they have a B1/B2 visa with the following names

Father's VISA
Last Name: AAAAA BBBBB
Given Name: CCCC DDDDD

Mother's VISA
Last Name: XXXXX YYYYY ZZZZZ
Given Name: FNU

Both their visas are valid till 12/2017

The above names match their old passport.

They recently got their passport renewed in India, and their new passport has the following names

Father's passport:
Surname: DDDDD
First Name: AAAAA BBBBB CCCC

Mother's passport:
Surname: ZZZZ
First Name: XXXXX YYYYY

My concern is the difference in their names between the visa/old passport and new passport. I am not sure how much of an issue this will be at the port of entry. Will they need to get a new visa? 

Please let me know.