Did Isaac know it was Jacob when he blessed him?

No. Genesis says he did not.

The narrator gives the verdict in plain words at Genesis 27:23:

וְלֹ֣א הִכִּיר֔וֹ כִּֽי־הָי֣וּ יָדָ֗יו כִּידֵ֛י עֵשָׂ֥ו אָחִ֖יו שְׂעִרֹ֑ת וַֽיְבָרְכֵֽהוּ

ve-lo hikkiro ki-hayu yadav ki-yedei Esav achiv se'irot va-yevarakhehu

"And he did not recognize him, because his hands were hairy like the hands of Esau his brother, so he blessed him." — Genesis 27:23

The verb is hikkir (הִכִּיר), from the root נכר (H5234) — «to recognize, to identify.» It is the same verb the brothers use when they bring Joseph's bloodied robe to Jacob and tell him to «recognize» it (Gen 37:32), and the same verb Tamar uses when she sends Judah's seal and staff back to him: «recognize, please, to whom these belong» (Gen 38:25). Each time the verb appears in Genesis, someone is being asked to identify a person from a token — and the answer is freighted.

At Genesis 27:23, Isaac fails the test. He does not recognize Jacob. The disguise works.

Two strands of later Jewish tradition tried to soften this. The pseudepigraphal book of Jubilees (mid-second century BC) adds a sentence not in Genesis: «and he discerned him not, because it was a dispensation from heaven to remove his power of perception» (Jubilees 26:18). The blinding was divine, not accidental — Jubilees protects Isaac by making the failure providential. A much later rabbinic midrash, Genesis Rabbah 67:4 (c. AD 200–500), takes the opposite tack and claims Isaac did recognize Jacob and blessed him anyway. Both readings are interpretive overlays; neither is in the Hebrew text.

The New Testament adopts neither. Hebrews 11:20 does not say «by faith Isaac saw through the deception.» It says simply:

Πίστει καὶ περὶ μελλόντων εὐλόγησεν Ἰσαὰκ τὸν Ἰακὼβ καὶ τὸν Ἠσαῦ

pistei kai peri mellontōn eulogēsen Isaak ton Iakōb kai ton Ēsau

"By faith, concerning things to come, Isaac blessed Jacob and Esau." — Hebrews 11:20

The faith is in Isaac's response after the deception — most directly in the trembling ratification at Genesis 27:33, where Isaac realizes what has happened and says gam barukh yihyeh («indeed, he shall be blessed»). The patriarch did not see through the disguise; he confirmed what the disguise had accomplished. Hebrews calls that faith — the recognition that what God had spoken before the twins were born (Gen 25:23, «the elder shall serve the younger») had landed where God intended, despite him.

Isaac's own word for what Jacob did seals the question. At Genesis 27:35 he names the deed:

בָּ֥א אָחִ֖יךָ בְּמִרְמָ֑ה וַיִּקַּ֖ח בִּרְכָתֶֽךָ

ba achikha be-mirmah va-yiqqach birkhatekha

"Your brother came with deceit and took your blessing." — Genesis 27:35

Mirmah (מִרְמָה, H4820) means «deceit, treachery.» Targum Onqelos translated the word as chokhmeta — «wisdom» — to soften the verdict. The Hebrew narrator chose deceit; the Aramaic synagogue chose wisdom. The New Testament makes its own decision by negation: Isaiah 53:9 says of the Servant of Yahweh, lo mirmah be-fiv — «no deceit in his mouth.» 1 Peter 2:22 cites that verse directly. The patriarch deceived; the Servant did not. The text never absolves Jacob.

For the full chapter — including the heel-trail from Jacob's birth-grasp to the lifted heel of the betrayer at John 13:18, and the seven-clause blessing that Balaam will reissue in reverse — read The Stolen Blessing: The Densest Blessing Chapter in the Canon.