His name spread far and wide, he gained a reputation, his name became renowned/ to become famous/ to attain worldwide fame
To become widely known; to gain a reputation.
("And he made in Jerusalem engines, invented by skillful men, to be on the towers and on the corners, to shoot arrows and large stones; and his name spread far and wide, for he was marvelously helped until he was strong" - II Chronicles 26:15, about King Uzziah), and likewise: "Abaye said to him: You have become famous, for you have been appointed head of the yeshiva, and your awe will be cast upon everyone" - Berakhot 56b)
Translation
Expression (Hebrew)
יָצָא שְׁמוֹ לְמֵרָחוֹק, יָצָא לוֹ שֵׁם, יָצָא שְׁמוֹ לִתְהִילָּה
Definition (Hebrew)
הִתְפַּרְסֵם בָּרַבִּים. יָצָא לוֹ מוֹנִיטִין.
("וַיַּעַשׂ בִּירוּשָׁלִַם חִשְּׁבֹנוֹת מַחֲשֶׁבֶת חוֹשֵׁב לִהְיוֹת עַל הַמִּגְדָּלִים וְעַל הַפִּנּוֹת לִירוֹא בַּחִצִּים וּבָאֲבָנִים גְּדֹלוֹת וַיֵּצֵא שְׁמוֹ עַד לְמֵרָחוֹק כִּי הִפְלִיא לְהֵעָזֵר עַד כִּי חָזָק"- דִּבְרֵי הַיָּמִים ב כו טוּ (עַל הַמֶּלֶךְ עֻזִיָּהוּ), וְכֵן:"לְאַבַּיֵּי אָמַר: יָצָא לְךָ שֵׁם שֶׁנַּעֲשֵׂית רֹאשׁ יְשִׁיבָה וְאֵימָתְךָ תְּהֵא מֻטֶּלֶת עַל הַכֹּל"- בְּרָכוֹת נוּ ע"ב)