One thing that just struck me, I remembered that episode where Paige gets to meet Elizabeth's mom, and she can barely pronounce Paige's name.

A lot of Christian names are more-or-less easily translated. But AFAIK, there's no Russian equivalent (at least no commonly used one) for either Paige or Henry?

The metaphor says: Elizabeth and Phillip gave their children names so American, that they can never become Russians under their own identity.