And why does it need to inform us the name of Pinchas' ancestors?
Ramban #1 (on Pasuk 23): Because she was a daughter (descendent) of Putiel - Yosef who struggled with (and overcame) his Yeitzer ha'Ra and Yisro, who fattened calves for Avodah-Zarah 1 (and gave it up in order to worship Hashem), 2 and it teaches us that via Pinchas, 3 who earned the Kehunah on his own merit, they merited everlasting Kehunah.
Ramban #2: Throughout Tanach, it is customary to mention the name of the king's mother. 4
Ramban: Bava Basra, 110a.
Ramban: Alternatively, Putiel was a well-known dignitary of that time, whom the Pasuk mentions here for praise because he was a righteous man.
Oznayim la'Torah: Pinchas inherited the strength to overcame the Yeitzer ha'Ra for Z'nus from Yosef and for Avodah Zarah, from Yisro
Why does the Torah use the expression 'from the daughter of Putiel?
Rashi: From the daughters of Yisro, who fattened calves (Pitem Agalim) for Avodah Zarah, and from the daughters of Yosef, who struggled (she'Pitpet) with his Yeitzer ha'Ra.
Ramban: Either because he had many daughters, of whom Elazar picked one, or because she was not a daughter, but a granddaughter of Putiel. 1
Ramban: Who was Misyaches after him because he was well-known, which also explains why her name is not mentioned.