I've never had a problem spotting friend from foe in this game, but yes, having one set of characters used by both teams is ridiculous. I can be playing as Boris, get shot by Boris and revived by another Boris. It's stupid.
BF5 had the right idea, if DICE insist on using named characters, then at least create a set for each side. Personally I'd prefer to go back to the anonymous soldier in BF 3 & 4 eras and be free to customise their outfit and loadout depending on their class.
I don't need to be playing as a character with a pointless back story, the person I'm playing as on screen is surely supposed to be an avatar representing ME?
In which case, give us a simple face editor, a couple of standard body types for male and female and let us kit them out how we want. That way you will get unique soldiers on both sides, identified by their faction specific outfits.