The Talmud states that Mordechai was called by several names, and that 'Mordechai' was his Babylonian name while 'Petachiah' was his Hebrew name — highlighting that even in exile he maintained a dual identity, one foot in the gentile world and one rooted in holiness.
רַבִּי יוֹחָנָן אָמַר: לְעוֹלָם מִבִּנְיָמִן קָאָתֵי, וְאַמַּאי קָרֵי לֵיהּ ״יְהוּדִי״? עַל שׁוּם שֶׁכָּפַר בָּעֲבוֹדָה זָרָה. שֶׁכׇּל הַכּוֹפֵר בַּעֲבוֹדָה זָרָה נִקְרָא ״יְהוּדִי״, כְּדִכְתִיב: ״אִיתַי גּוּבְרִין יְהוּדָאיִן וְגוֹ׳״.
Rabbi Yoḥanan said a different explanation of the verse: Actually, Mordecai came from the tribe of Benjamin. Why, then, was he referred to as Yehudi? On account of the fact that he repudiated idol worship, for anyone who repudiates idolatry is called Yehudi. It is understood here in the sense of yiḥudi, one who declares the oneness of God, as it is written: “There are certain Jews [Yehuda’in] whom thou hast appointed over the affairs of the province of Babylonia, Shadrach, Meshach, and Abed-Nego; these men, O king, have not regarded you: They serve not your gods, nor worship the golden image which you have set up” (Daniel 3:12). These three individuals were in fact Hananiah, Mishael, and Azariah, who were not all from the tribe of Judah but are referred to as Yehuda’in because they repudiated idol worship.