Well, if you're converting, then you must have a Rabbi that you're studying under. I'd ask for their opinion, or at least the opinion of someone knowledgeable at your synagogue. The Rabbi at least would know what is Kosher.
It is true that names like Neta, Noy, and Sapir are all names much more common in modern Israeli culture. However, I'm not sure if that's technically disqualifying. They all are Hebrew, after all. I think that perhaps her dislike may not be on the grounds of religious law, but her own personal dislike. I say this because I think these names were just nouns prior to being used as proper names. For example, Sapir is just a sapphire (similar since our word's etymology comes from Semitic roots) and she may dislike that just as she'd dislike someone here in America (or wherever you are) naming their kid Apple. Essentially, a lot of "Israeli" names are just nouns made first names. Of course, a LOT of the historic Hebrew names doubled as nouns as well, like Caleb (dog), Hadassah (myrtle tree) and even Pnina (pearl). So, from this standpoint, I really don't see why your names should be unacceptable, even if they're more utilized by modern secular Israelis.
Another thing to point out is that there are cases where Hebrew names are, well, not Hebrew. Esther comes from the Persian word for star, unsurprising since Farsi is an Indo-European language and related to the Greek word for star, aster (as from that, astrology and asteroid). I believe even Alexander can count as a Hebrew name, if I'm remembering things correctly, since Alexander the Great earned huge admiration from Jews. I point this out because I also take issue with one other thing she says: That these names are "not Jewish". While there is criteria for choosing a Hebrew name, Jews can have any name they want. I'm a Jew, and my Hebrew name and my real name not normally of Hebraic roots aren't the same, after all. I'm aware that she may not be talking about that and her wording (or your recall of it) may have been poorly stated, but it is worth noting that many Orthodox Jews don't have Hebrew first names anyway.
If this friend means a lot to you, and the name isn't something you focus on too heavily, then do know that Yael, Esther and Pnina should all work well. With Esther and Yael at least, I know that they're Biblical characters so there should be 0 objection. You could search a bit more and see if there are names that work for both of you that are close or have similar meanings, for example switching out Sapir for Tzippora (it's a Biblical Hebrew name meaning bird) or Noy with Ziva, since their meanings seem close enough. Or you can do what I would in your shoes: Ignore her, it's YOUR name. Thank her if she's pointing out a violation with the rules, something I don't think you're in, if there is one; but, if once again all your choices are Kosher, then it's not her place to shoot them down.