Because Jacob encountered God (YHWH) that Night
The Meaning of Face to Face
The phrase "face to face" in the Hebrew (פָּנִ֣ים אֶל־פָּנִ֔ים) uses the plural form of the word פָּנֶה (paneh; "face").1 However, it would not necessarily be proper to translate it then "faces to faces," because the word is always found in the plural form in Hebrew.2 This is because Hebrew uses plurality to express compound objects ("a single object that consists of several parts").3
In the context of personal interaction, while the expression can mean literally facing one another to the face (e.g. Jer 32:4, 34:3), it also has the idea of "appearing before,"3 as when all Israel was "face to face" with God at Sinai (Dt 5:4). But the term "face" more figuratively was simply an expression of the "presence" of a person,4 including God (e.g. Ex 33:14-15).
The expression when used of interacting (seeing, speaking, etc.) with God refers to "a form of the LORD," (תְּמוּנָה; "likeness" or "representation")5 as was the case with Moses' interaction with God "face to face" (Num 12:8; cf. Ex 33:11, Dt 34:10). Such is known as a theophany.
Thus while seeing God's face (as in God's full glory) all men were incapable of doing and surviving (and so Moses did not even see Him so; Ex 33:18-23), God could manifest Himself in His creation in other ways that "localized" His presence, and one could interact with Him in a "face to face" manner, but not be expressing His full glory.
That the one encountered was God (YHWH)
We have seen that Moses interacted "face to face" with God through a "form" in which God appeared to Moses. The same is happening here in Genesis 32:24-30. There it refers to the one Jacob wrestled with as "a man" (v.24).
But in the passage, this "man" Jacob sensed was no mere man, but something more. No doubt it was in part because of the wrestling, but also because Jacob knew God had another base of operations near his own camp here.
So Jacob sought this "man's" blessing, which was granted--his new name, "Israel," which this "man" reveals is given because Jacob had "struggled with God and with men, and have prevailed" (v.28; NKJV). The name is believed to come from the Hebrew root שׂרה (srh), which can mean either (1) "to persist, exert, persevere" the idea being contend or fight, or it can mean (2) "rule",6 and the suffix אֵל (el; "God"). Hence the two common routes it is translated: "fights/contends/prevails with God" or "rules with God/prince of God."
So it is this "man" that reveals Himself as God to Jacob by the activity of the night and the name given. Jacob seeks confirmation of this, but the "man" is elusive (v.29; cf. Jud 13:17-18). This apparently only convinced Jacob more that it was God whom he had wrestled with (v.30).
Hosea 12:3-4 tells us that this "man" was indeed not only a מַלְאָךְ (melek; "angel" or "messenger," v.4), but was "God" (v.3) Himself as the messenger, the very same God (YHWH) that Jacob had met in Bethel (v.4; cf. Gen 28:13).
The "man" Himself cryptically revealed that He was God, Jacob testifies that it was God, Moses records in Scripture for us that it was God, and Hosea confirms it was God.
It is God (YHWH) that Jacob wrested with, in the form God appeared to him as (a man), and that is why Jacob names the place Peniel.
1 Francis Brown, Samuel Rolles Driver, and Charles Augustus Briggs, Enhanced Brown-Driver-Briggs Hebrew and English Lexicon (Oak Harbor, WA: Logos Research Systems, 2000), s.v. פָּנָה. Hereafter referred to as BDB.
2 R. Laird Harris, Gleason L. Archer Jr., and Bruce K. Waltke, eds., Theological Wordbook of the Old Testament (Chicago: Moody Press, 1999), #1782.
3 Labeled as a "plural of extension" in Ronald J. Williams, Williams' Hebrew Syntax, 3rd. ed. (Toronto: University of Toronto Press, 2007), 3.
4 BDB, s.v. פָּנָה.
5 BDB, s.v. תְּמוּנָה.
6 BDB, s.v. שָׂרָה. See also Ludwig Koehler, Walter Baumgartner, M. E. J. Richardson, and Johann Jakob Stamm, The Hebrew and Aramaic Lexicon of the Old Testament (Leiden; New York: E.J. Brill, 1999), s.v. יִשְׂרָאֵל.