You are overthinking it.
First, minimize the number of times someone would even HAVE to use a proper name. In the real world, how often do you use someone's name during a conversation with that person? One of the things I often do when editing is removing unneeded references to proper names. One it is established that a person thinks the girl is so-and-so, you don't need to keep addressing the fact.
Second, if the girls are in two different time periods, then the situational changes with the time periods will serve as the notice to readers that they are currently at the POV of a specific girl.
Third, trust your readers to be smart enough to follow the story. Keep it simple, and the reader will be able to follow along. The more you overthink it and artificially try to make it understandable, the more likely it will confuse people.
This is no different then when dealing with characters in disguise who are pretending to be someone else, or cases of mistaken identity.
First, minimize the number of times someone would even HAVE to use a proper name. In the real world, how often do you use someone's name during a conversation with that person? One of the things I often do when editing is removing unneeded references to proper names. One it is established that a person thinks the girl is so-and-so, you don't need to keep addressing the fact.
Second, if the girls are in two different time periods, then the situational changes with the time periods will serve as the notice to readers that they are currently at the POV of a specific girl.
Third, trust your readers to be smart enough to follow the story. Keep it simple, and the reader will be able to follow along. The more you overthink it and artificially try to make it understandable, the more likely it will confuse people.
This is no different then when dealing with characters in disguise who are pretending to be someone else, or cases of mistaken identity.