And why does it need to inform us the name of Pinchas' mother?
Ramban #1 (on Pasuk 23): Because she was the daughter 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, 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. 3
Why does the Torah use the expression 'from the daughter of Putiel?