I am curious, as to why a parent would name a daughter, Batsheva?

We see that David HaMelech, undoubtedly one of the outstanding figures in the entire Tanach, felt extremely close to Batsheva, and trusted her more than any of his 17 other wives. It’s also significant that he promised her to choose her son Shlomo, as his heir and continuation. Our rabbis in the midrash view her very positively, being a good influence and religious advisor to Shlomo, despite his being the wisest of all men, and even after he was already king (e.g. Sanhedrin 70b; Yalk.Sh. Mish. 964). Many even explain that Shlomo wrote the “Eshet Chayil” (Mishlei 31) about the ideal woman of Israel, as a poem in admiration of his mother, Batsheva! In short, she’s surely a woman to emulate, and that would warrant naming children after her, no matter what the meaning of her name. If you’re asking about the meaning of her name (literally: “the daughter of seven”) and why her parents named her that: some explain that she was the 7th daughter/child, others, that she was born on Shabbat (the 7th day) or Tishrei (the 7th month). Notice that in Divrei HaYamim (Chron. I, 3, 5), she’s called Bat-Shu’a, like Yehuda’s wife (Breishit 38, 12), so it must have been a common name, short for Bat-Y’shua, the daughter of redemption/deliverance (perhaps after a difficult birth?). Shabbat Shalom! Rav Ari Shvat