Is the derivation of the name Putiel knowable?

Summary: Can we know the derivation of the name Putiel? A four-way machlokes between Rashi, Ibn Ezra, Ibn Caspi, and Shadal reveals something about their methodology, and their approach to peshat.

Post: A genealogical list in parashat Vaera includes a fellow named Putiel. Shemot 6:25:

כה  וְאֶלְעָזָר בֶּן-אַהֲרֹן לָקַח-לוֹ מִבְּנוֹת פּוּטִיאֵל, לוֹ לְאִשָּׁה, וַתֵּלֶד לוֹ, אֶת-פִּינְחָס; אֵלֶּה, רָאשֵׁי אֲבוֹת הַלְוִיִּם--לְמִשְׁפְּחֹתָם.

25 And Eleazar Aaron's son took him one of the daughters of Putiel to wife; and she bore him Phinehas. These are the heads of the fathers' houses of the Levites according to their families.

Who in the world is Putiel, and why should we care about the name of the father-in-law of Eliezer? Rashi writes:

[one] of the daughters of Putiel-: Of the seed of Jethro, who fattened (פִּטֵּ ם) calves for idolatry (see Rashi on Exod. 2:16) and [who was also] of the seed of Joseph, who defied and fought (פִּטְפֵּט) against his passion [when he was tempted by Potiphar’s wife]. — [from B.B. 109b]		מבנות פוטיאל: מזרע יתרו שפטם עגלים לעבודה זרה. ומזרע יוסף שפטפט ביצרו:

The gemara in Bava Batra 109b-110a:

R. Eleazar said: One should always associate36  with good [people]; for behold, from Moses who married the daughter of Jethro,37  there descended Jonathan38  [while] from Aaron, who married the daughter of Amminadab, there descended Phinehas.39  But did not Phinehas descend from Jethro? Surely it is written, And Eleazar40  Aaron's son took him one of the daughters of Putiel to wife;41  does not this mean that he descended from Jethro who crammed42  calves for idol worship? — No; [it means] that he descended from Joseph who conquered43  his passions.44  Did not, however, the tribes sneer at him and say.45  'Have you seen this Puti-son?46  A youth whose mother's father crammed calves for idol-worship should kill the head47  of a tribe in Israel!'
But [this is really the explanation], if his mother's father [descended] from Joseph, his mother's mother1  [descended] from Jethro; if his mother's father [descended] from Jethro, his mother's mother [descended] from Joseph.2  [This may] also [be confirmed by] deduction, for it is written, of the daughters of Putiel, from which two3  [lines of ancestry]4  are to be inferred.

Rashi thus adopts the conclusion of the gemara, that we are to infer two lines of ancestry.

This addresses a peshat concern of just who this character is. He was someone who came out of nowhere, and Rashi likes his Biblical narrative extremely closed-canon. It must be someone we know from elsewhere. Plus, also, this also makes the random genealogical note into something meaningful.

Ibn Ezra makes a seemingly innocuous comment, which only becomes pointed when we consider the midrash and Rashi as background. He writes:

פוטיאל -
היה מבני ישראל ולא ידענו טעם פוטיאל כאשר לא ידענו טעם למישאל וכל שמות הנזכרים כמו אהרן. ולולי נכתב מעשה משה, לא היינו יודעין למה נקרא כן.

He was from the children of Israel. And we do not know the reason for Putiel, just as we do not know the reason for the name Mishael, or all of the names mentioned, such as Aharon. And were the incident with {the saving} of Moshe not written, we would not have known why he was called this.

By saying he was from the Bnei Yisrael, he is rejecting the idea that this is a reference to Yosef, a son of Yaakov; and that this is a reference to Yisro, who was not an Israelite. And he is not just innocently saying that he does not know the answer as to the etymology, but that Rashi cannot know it either. And that Chazal as well do not know it. He thus rejects the idea that this is some Sinaitic tradition, or that one can use the type of sevara used in the gemara to figure this type of thing out. We don't know why this random person was named Putiel, and one can adopt an open-canon approach, and not consider this a burning question which must, or even can, be addressed by a pashtan.

Ibn Caspi echoes this thought:

והגה פוטיאל היה מבגי ישיאל אדם גדול ידוע אצלם, כמו
עמינדב שקדם זכרו. אולם למה גקרא שמו ם־טיאל לא ידעגי כמו
ועמיגדב ואליעזר ואיתמר וזולת זה, C שלא גדע למה הוא י שם אהרן
• בי אין אגהגו גכיאים, ואגו אין לגו לדקדק במה שכתוב בשפר 5

He effectively echoes Ibn Ezra. His twist is one of intended audience. While we may have no way of knowing who in the world he was, we can intuit that it must have meant something to them, the ancient Israelites. But we, the pashtanim, are not neviim, and so should not give our own explanations as to the derivation of the name.

Shadal meanwhile tries to give an etymology of the name! He writes:

כה] פוטיאל: נראה מורכב ממילה מצרית פוטי (עיין בראשית ל"ז ל"ו) ומשם אל בלשון הקדש, וענינו מיוחד לכבוד האל (בני בכורי זצ"ל).נ

Thus,  it seems to be of the pattern of a clearly Egyptian name we see, Potifar and Potifera. And thus, it means dedicated to the honor of the god. And so we then have the Hebrew equivalent of the name. I've seen similar explanations elsewhere. Namely, that Poti-fe-Ra should be processed as gift-from-Ra, the Sun god. Puti-El would then be like Netanel, Gift of God. If so, this, along with the name Achi-Ra ben Einan, would be a counterexample to the idea that the Israelites did not change their names in Egypt.