Found out recently that צרויה as in (Yoav Ben Tzruyah) was actually Yoav’s mom and not his father. Why is Yoav constantly referred to as the son of his mother, when the Tanach norm is to use their fathers' name? And what do we know of Tzruya? Any midrashim mention her?
In the commentary by the anonymous student of Rasag to Divrei Hayamim 1:2:16 he writes:
""and their sisters Tzruyah and Avigail" - And Tzruyah's husband was S'rayah, and not S'rayah who fathered Yoav, father of Gei Charashim (DH 1:4:14), but S'rayah son of Asael who lived in the time of David, and for this reason he named his son Asael, brother of Yoav,1 after his father Asael.2
His emphasis regarding the identity of S'rayah is interesting because Rav Hai Gaon wrote (Shaarei Teshuva (Teshuvot Ha'geonim), Siman 19):
"And that which you asked regarding Yoav ben Tzruyah, why was he named after his mother, for his father's name is known, as it says "S'rayah begot Yoav, father of Gei-Charashim", but since his mother was the sister of the king, he was named after her, so that his greatness would rise out of her..."3
So we see that in the Gaonic period there were two rival traditions regarding the identity of Yoav's father: Both knew his name was S'rayah, but there were disagreements on which person in Tanach the name referred to. In any case, we learn from Rav Hai's statement that Yoav was named after his mother because her yichus was more impressive than his father's. The rest of the siman includes other examples of this.
Similarly, Rabbi Yitzchak Notovitz wrote in Shulchan Ha'ma'arechet, Introduction, 4:
"It is the way of the text to attribute people after their brothers who are more important than them, such as "older brother of Yefet" (Beresheet 10:21), "wife of Nachor, brother of Avraham" (ibid 24:15), and among women: "sister of Nachshon" (Shemot 6:23), "sister of Aharon" (ibid 15:20), as well as attributing a man after his mother, [such as] Betuel son of Milkah, wife of Nachor (ibid 24:15), Avishai son of Tzruyah and Yoav son of Tzruyah, Yesha'yah son of Atalyah (Ezra 8:7), and so on."
More info on Tzruyah:
Her name, which might be a fusion of Tzori (balm) and the name of Hashem, is one of the circa 60 personal names containing contracted forms of the name of Hashem from the time of David and Shlomo (for more info, see Prof. Yoel Elitzur's essay here, in particularly nn. 16-17).
According to Malbim on DH 1:2:15, Tzruyah and Avigail were step-daughters of Yishai. Their biological father was named Nachash. After he died, his wife married Yishai. However, according to the gemara in Bava Batra 17a and Shabbat 55b, "Nachash" was a nickname for Yishai.
1 One of Yoav's brothers, killed by Avner (Shmuel 2:2:18-23).
2 It should be noted that the commentator spells S'rayah's father's name as עשהאל, like his Yoav's brother, but in our Tanachim we have עשיאל as the father's name.
3 This would make Yoav and his siblings the nephews of Otniel ben Kenaz. Incidentally, according to the gemara in Temurah 16a, Otniel's real name was Yehudah and his brother's name was Shimon. This is likely a reference to Shoftim 1:3, usually taken as a reference to the entirety of the tribe of Yehudah and the entirety of the tribe of Shimon, despite the use of singular forms.
She was Dovid Hamelech’s sister as the passuk in Divrei Hayomim 1:2:16
וְאַחְיֹתֵיהֶ֖ם צְרוּיָ֣ה וַאֲבִיגָ֑יִל וּבְנֵ֣י צְרוּיָ֗ה אַבְשַׁ֛י וְיוֹאָ֥ב וַעֲשָׂהאֵ֖ל שְׁלֹשָֽׁה׃
ואחיותיהם צרויה ואביניל. מפני כבודו של דוד שהיו בני אחותו גבורים ואנשי חיל ושרים כך מפורש:
The Malbim [IISamuel 17-25] (https://www.sefaria.org.il/II_Samuel.17.25?lang=he&p2=Malbim_on_II_Samuel.17.25.1&lang2=he) writes about Yoav (and his two brother) כי אביו לא נודע בשם. This could either mean that his name wasn't known, or that he wasn't even worth mentioning by name. The Metzudas Dovid (https://www.sefaria.org.il/II_Samuel.17.25?lang=he&p2=Metzudat_David_on_II_Samuel.17.25.4&lang2=he&w2=all&lang3=he) there suggests as a possibility that Tzeruya was a half-sister of David, as David's mother had previously been married to someone called Nachash, and Tzeruya & Avigail (mentioned in that Pasuk) were daughters of that marriage.