Henry they'd probably just pronounce as Genry. So yeah, different name, but with that small change it would be pretty smooth. Even closer in pronunciation than some names that have translations, like Michael vs. Mikhail.

I remember the grandmother struggling with the vowel in Paige, though. I think that would be harder. There wouldn't, imo, be an obvious Russian way to say it and that vowel seems to be the stumbling block. Plus I would bet that your average Russian person is at least more familiar with the name Henry than Paige.

Makes me remember also when Paige asks her parents' real names. Philip gives the very American-friendly short form of his name. Elizabeth gives her full name that Paige stumbles over immediately. (And Keri Russell carefully then pronounces it for her...wrong.)