(Genesis 32:33) "Therefore the children of Israel do not eat the sinew of the thigh-vein." Rabbi Chanania said: Why is its name called gid hanasheh? Because it slipped (nashah) from its place. Rav Huna said: This twisted strand of the sinew is itself permitted, but Israel are holy and forbade it upon themselves. Rabbi Yehudah and Rabbi Yose: Rabbi Yehudah says: He touched one of them, and one of them became forbidden. Rabbi Yose says: He touched one of them, and both became forbidden. There is a teacher who taught that reason decides it is the right one, in accordance with Rabbi Yehudah, and there is a teacher who taught that it is the left one, in accordance with Rabbi Yose. The one who says reason decides it is the right one [cites] (Genesis 32:26), "and he touched the hollow of his thigh"; and the one who says reason decides it is the left one [cites], "when he touched the hollow of Jacob's thigh."
Why the Sinew Is Called the Gid Hanasheh and Which Side
Yalkut Shimoni on Torah 133:6
(בראשית לב לג) עַל כֵּן לֹא יֹאכְלוּ בְנֵי יִשְׂרָאֵל אֶת גִּיד הַנָּשֶׁה. אָמַר רַבִּי חֲנַנְיָא, לָמָּה נִקְרָא שְׁמוֹ גִּיד הַנָּשֶׁה, שֶׁנָּשָׁה אֶת מְקוֹמוֹ. רַב הוּנָא אָמַר, הֲדֵין פְּקוּקְלָתָא דְּגִידָא שָׁרְיָא וְיִשְׂרָאֵל קְדוֹשִׁים הֵן וְאָסְרוּ אוֹתָהּ עֲלֵיהֶן. רַבִּי יְהוּדָה וְרַבִּי יוֹסֵי, רַבִּי יְהוּדָה אוֹמֵר, בְּאַחַת מֵהֶן נָגַע וְאַחַת מֵהֶן נֶאֶסְרָה. רַבִּי יוֹסֵי אוֹמֵר, בְּאַחַת מֵהֶן נָגַע וּשְׁתֵּיהֶן נֶאֶסְרוּ אִית תָּנָא תָּנִי, הַדַּעַת מַכְרַעַת שֶׁהִיא שֶׁל יָמִין כִּדְרַבִּי יְהוּדָה, וְאִית תָּנָא תָּנִי שֶׁהוּא שֶׁל שְׂמֹאל כִּדְרַבִּי יוֹסִי. מַאן דְּאָמַר הַדַּעַת מַכְרַעַת שֶׁהוּא שֶׁל יָמִין (לעיל פסוק כו) "וַיִּגַּע בְּכַף יְרֵכוֹ" וּמַאן דְאָמַר הַדַּעַת מַכְרַעַת שֶׁהוּא שֶׁל שְׂמֹאל כִּי נָגַע בְּכַף יֶרֶךְ יַעֲקֹב.