A little thing's been bugging me about Paige, and I wonder if it's symbolic or something on the writers' part: it's the fact that she's the only one in the Jennings family with a name that has no Russian equivalent whatsoever. The Jennings have probably known all this time that there's a chance they will be deported from the country with the kids in tow, so giving them names that work in both countries would make sense. And there are a ton of names that are used in the US and Russia as well without being obviously one or the other. (I mean, Philip and Elizabeth can even still be Philip and Yelizaveta in Russia, which were my late uncle and grandmother's respective names.) Alice, for example, would never point directly to Russian origins, but while rare, there were/are Russian Alisas. There's Eve, Joan, Mary, Anne, Rose, Lily, Amelia, etc.
Henry's name in Russia would be Genrikh, which sounds a little too German for post-war Russia, but he'd probably adjust to being called Gehna quickly enough (almost no one in Russia is referred to by their full name by anyone close to them. In season 1's finale, even though her mother does call her Nadezhda at one point, Elizabeth's mother starts her taped letter adressing her as "Nadinka", and I'm sure she was called Nadia throughout her whole childhood. And there's absolutely no way Philip has "Misha" on his birth certificate. His real name is almost definitely Mikhail/Michael.)
Paige would have to choose a brand new name in Russia if it came to that, and her parents could have saved her that trouble by choosing any number of names that converted well. So why choose "Paige", which has a completely English root? From what I can tell it wasn't a particularly popular name in the 80s US.