Why did he ask "why do you ask my name"?
Ralbag (16, 20): Really, it was a Navi; two people do not have prophecy together like this (hear from an angel). It seems that it was Pinchas. 1 He did not give his name, nor eat the kid, to strengthen their belief [afterwards] that he is an angel, so they would carefully follow his words.
Malbim: I do not seek honor and glory from people, for I am an angel.
Perhaps he did not want to give his name for the same reason as the angel that fought with Yakov (PF). Refer to Bereishis 32:30:2:1-3, 9, 32:30:2:3*.
Tanchuma says that Pinchas could make himself invisible (refer to Yehoshua 2:4:1:2). According to the opinion that Pinchas is Eliyahu, often Ru'ach Hashem would carry him away (Melachim 1:18:12), and he became Mal'ach ha'Bris. Chazal say that Pinchas lost his Ru'ach ha'Kodesh after the episode with Bas Yiftach (refer to 12:7:1:1*), but perhaps this prophecy was before that. Shimshon became the Shofet 25 years after Yiftach died (Avtzan, Eilon ha'Zevuloni
What is "Feli"?
Rashi (from Sifri Nasa 42): It is covered. It always changes, and it is not known to what it will change today.
Radak: The Aleph is hidden (has no vowel), and the Yud is Leyaches (to attribute to Pele, wondrous). If the Aleph was 'seen' (had a vowel, the vowels of the entire word) would be like the word 'Ivri', and it would mean covered and hidden, that one cannot know it.
Radak citing Targum Yonasan: It is Mefarash. Also the Targum of "Ki Yafli" (Bamidbar 6:2) is Arei Yafrish. It is separated from your knowing it.
Malbim #1: It is something that beings that dwell in physicality cannot know.
Malbim #2: An angel's name is according to his mission. At this moment he is sent to do wonders, like it says "Mafli La'asos" (verse 19). Now his name is Peli.
Malbim citing Bamidbar Rabah 10:5: He was called Peli due to Nezirus - "Ki Yafli Lindor Neder" (Bamidbar 6:2).
