No, while not something everyone will be familiar with there’s nothing about it that sounds fake. I’d guess that some people may struggle with using the full name at first, but it shouldn’t be that hard to get used to.
[name_f][/name_f]
It does seem a bit close and I feel like I hear it a lot more than I used to. While [name_f]Lola[/name_f] is somewhat trendy right now (at least in the US) and shares sounds with a lot of popular names, I think it still stands out because it has a more distinctive vibe to me than the others you mentioned.
[name_f][/name_f]
I debated voting for this one because of its uniqueness and similar feel to [name_f]Beatrix[/name_f]. It’s certainly the least familiar of the six and probably least likely to ever surge in popularity.
[name_f][/name_f]
[name_f]Pretty[/name_f] solidly 4 syllables to me, and does seem a bit more modern than the others, but still fits your criteria well and pairs really naturally with [name_f]Beatrix[/name_f].
[name_f][/name_f]
I don’t notice it but if it bothers you a lot I might look for something else, also seems very [name_m]Harry[/name_m] [name_m]Potter[/name_m] to me paired with [name_f]Beatrix[/name_f] (with its similarity to Bellatrix)
[name_f][/name_f]
Not a bad choice, but for me personally, the vibe is SO similar to [name_f]Beatrix[/name_f] that doesn’t stand out as much