Why was Jacob renamed Israel?
Because he had «striven with God and with men and prevailed» — the name Israel is built from the verb «strive» (sarah) plus El, «God.» The Hebrew witnesses are unanimous on this striving sense; the later idea that Israel means «the man who sees God» is a Greek-Jewish allegory with no footing in the letters of the name. God renames at covenant thresholds, as he did with Abram and would later with Simon.
When the wrestler asks Jacob's name and Jacob answers «Yaaqov» — the heel-grabber, the supplanter — the man gives him a new one that reverses his whole biography.
The name says «strive»
לֹא יַעֲקֹב יֵאָמֵר עוֹד שִׁמְךָ כִּי אִם־יִשְׂרָאֵל כִּי־שָׂרִיתָ עִם־אֱלֹהִים וְעִם־אֲנָשִׁים וַתּוּכָל
lo Yaaqov… ki im-Yisrael ki-sarita im-Elohim ve-im-anashim va-tukhal
«Your name shall no longer be Jacob but Israel, for you have striven with God and with men, and have prevailed.» — Genesis 32:28
The name Yisrael (יִשְׂרָאֵל, H3478) joins the verb sarah (שָׂרָה, H8280) — «to persist, contend, prevail» — to El, «God.» And the text glosses itself with a second verb, va-tukhal, «and you prevailed» (from yakhol, H3201). Israel means the one who strove with God and overcame. The strive-verb sarah stands in only two verses in all of Scripture — here, and in Hosea's retelling of this same night (Hosea 12:3) — so the word is bound entirely to Jacob.
The Hebrew is unanimous; the «seeing» reading is later
The competing idea — that «Israel» means «the man who sees God,» as if from ish ra'ah El — has no footing in the Hebrew letters. The name carries no «see» root. The Masoretic text, the Hosea retelling, and the pre-Christ Dead Sea Hosea scroll all read sarah plus El, «strive with God.» The Septuagint, too, stays inside the striving register, rendering the verb «you prevailed, you grew strong with God.» The «seeing God» reading is a later Hellenistic-Jewish allegory (Philo; the Prayer of Joseph) — worth knowing as the later tradition it is, not set co-equal with the grounded Hebrew.
The pattern of the new name
This is not the first renaming the reader has seen, and it follows a fixed shape. God renamed Abram with the same construction: «your name shall no longer be called Abram, but your name shall be Abraham» (Genesis 17:5). He will re-give Jacob the name Israel directly at Bethel (Genesis 35:10). God renames at covenant thresholds, and the new name encodes the bearer's relation to him — the supplanter becomes the one who clings to God and prevails.
For the full account — the witnesses on the name, Hosea's reading of the wrestling, and the «seeing God» allegory weighed against the Hebrew — read The Wrestling at Peniel: The Grasper Becomes Israel.
What does Peniel mean, and how did Jacob see God and live?
Peniel means «the face of God» — Jacob named the place because «I have seen God face to face, and my life was delivered.» That survival is the marvel: elsewhere God tells Moses «no man shall see me and live.» The same rescue-verb Jacob had begged for against Esau comes back here in the passive — the deliverance he asked for from his brother arrives as deliverance from the encounter with God himself.
Who was the man who wrestled with Jacob at Peniel?
The narrator calls him simply «a man,» but Jacob says he saw God «face to face,» and the prophet Hosea later names the same wrestler both «God» and «the angel.» Genesis lets all three labels — man, God, angel — stand side by side without flattening them, and Jacob himself fuses two of them at the end of his life when he blesses Joseph's sons by «the Angel who redeemed me.»
Why did Jacob limp after wrestling at Peniel?
Because the man he wrestled touched the socket of his hip and wrenched it out of joint — so Jacob walked away from the encounter blessed but marked. The limp-word that describes him surfaces again only in the prophets, always for «the lame» whom the LORD gathers and saves. The wounded-but-blessed patriarch becomes the canon's picture of the limping remnant God draws in.