I think this is why they requested the NBI clearance to have her name on the birth certificate appear instead of the name on the passport. BC always trumps any other form of identification. Whatever name they decide to put in her visa, for as long as she has a copy of her birth certificate along with her passport, wala sigurong magiging problema.
I've traveled to the US with conflicting names (name in my visa still has my maiden name because I wasn't married yet when it was issued and my latest passport bears my married name) and it didn't become a problem. The website of the US embassy here in Manila suggested to bring along another form of identification, which in my case was my marriage certificate, in case immigration would question the conflict in names. But upon entry to the US, the immigration officer didn't even bat an eyelash that my names were different.
Congratulations tabs on your PPR and just go through the motions of this. Before you know it, PPV ka na at paalis ka na din just like the rest of our forum-mates here. Try also to check if the online application for NBI clearance is already up and running. And just a suggestion, don't go to the NBI Main Office kasi nightmare ata kumuha ngayon dun because of the new system they're putting up. Best to go to their satellite offices in the malls. We went to Robinson's Place in Manila but I believe they also have one in Galleria.
HTH...Good luck!
And thank you for sharing your experiences here.