Another interpretation: "Soco" - because he turned aside the punishment from coming into the world; "the father of Socoh" - for he was the father of the prophets who gaze [sochin] by the holy spirit; in Arabia they call a prophet "sochaya." "Jekuthiel" - because he made the children hope [mekavvin] in their Father in heaven. "The father of Zanoah" - he came and made them put aside [hizniḥan] that sin, as it is written, "And he scattered it upon the water" (Exodus 32:20). "And these are the sons of Bithiah" (1 Chronicles 4:18) - the Holy One, blessed be He, said to her: He was not your son, yet you called him your son; you too are not My daughter, yet I call you My daughter. "Whom Mered took" - this is Caleb. He rebelled [marad] against the counsel of the spies, and she rebelled against the counsel of her father; let the rebel come and take the rebellious woman. He saved the flock and she saved the shepherd. Rabbi Judah son of Rabbi Ilai says: Tobiah was also his name, as it is written, "And she saw that he was good [tov]" (Exodus 2:2). Rabbi Ishmael son of Rabbi Ami said: Shemaiah was his name, as it is written, "And Shemaiah son of Nethanel the scribe wrote them down" (1 Chronicles 24:6). Shemaiah - because God heard [shama el] his prayer. "Son of Nethanel" - a son to whom the Torah was given [nittenah] from the hand of God. "The scribe" - because he was the scribe of Israel. "The Levite" - because he was from the tribe of Levi. "Before the king and the princes" - before the King of the kings of kings, the Holy One, blessed be He, and His court. "And Zadok" - this is Aaron the priest. "And Ahimelech" - because he was the brother of a king. "Son of Abiathar" - a son on whose account the Holy One, blessed be He, forgave [vitter] the matter of the calf. Rabbi Joshua son of Korha says: Levi was also his name, after the root of his family. And Moses - behold, ten. The Holy One, blessed be He, said to Moses: By your life, of all the names you have, I call you only by the name that Bithiah, daughter of Pharaoh, called you, "and she called his name Moses" (Exodus 2:10). Hence, "And He called to Moses."
More Names of Moses and Why God Called Batya His Daughter
Yalkut Shimoni on Torah 428:5
דָּבָר אַחֵר שֶׁהֶעֱבִיר הַפֻּרְעָנוּת מִלָּבוֹא לָעוֹלָם, "אֲבִי סוֹכוֹ", שֶׁהָיָה אֲבִיהֶן שֶׁל נְבִיאִים שֶׁסּוֹכִין בְּרוּחַ הַקָּדוֹשׁ, בַּעֲרַבְיָא צַוְחִין לְנָבִיא סוֹכָיָא "יְקוּתִיאֵל" שֶׁעָשָׂה אֶת הַבָּנִים מְקַוִּין לַאֲבִיהֶן שֶׁבַּשָּׁמַיִם "אֲבִי זָנוֹחַ", בָּא וְהִזְנִיחָן מֵאוֹתָהּ עֲבֵרָה, הֲדָא הוּא דִכְתִיב "וַיִּזֶר עַל פְּנֵי הַמַּיִם" "וְאֵלֶּה בְּנֵי בִּתְיָה" אָמַר לָהּ הַקָּדוֹשׁ בָּרוּךְ הוּא לֹא הָיָה בְּנֵךְ וּקְרָאתוֹ בְּנֵךְ אַף אַתְּ לֹא בִּתִּי וַאֲנִי קוֹרֵא אוֹתָךְ בִּתִּי (דברי הימים שם) "אֲשֶׁר לָקַח מָרֶד", זֶה כָּלֵב, זֶה מָרַד בַּעֲצַת מְרַגְּלִים, וְזוֹ מָרְדָה בַּעֲצַת אָבִיהָ, וּבָא מוֹרֵד וַיִּקַּח אֶת הַמּוֹרֶדֶת. זֶה הִצִּיל אֶת הַצֹּאן וְזוֹ הִצִּילָה אֶת הָרוֹעֶה. רַבִּי יְהוּדָה בְּרַבִּי אִלְעַאי אוֹמֵר אַף טוֹבִיָּה הָיָה שְׁמוֹ, הֲדָא הוּא דִכְתִיב "וַתֵּרֶא אֹתוֹ כִּי טוֹב הוּא". רַבִּי יִשְׁמָעֵאל בְּרַבִּי אָמִי אָמַר שְׁמַעְיָה שְׁמוֹ, דִּכְתִיב (דבהי"א כד, ו) "וַיִּכְתְּבֵם שְׁמַעְיָה בֶן נְתַנְאֵל הַסּוֹפֵר" שְׁמַעְיָה שֶׁשָּׁמַע אֵל תְּפִלָּתוֹ. "בֶּן נְתַנְאֵל" בֵּן שֶׁנִּתְּנָה לוֹ תּוֹרָה מִיַּד אֵל. "הַסּוֹפֵר" שֶׁהָיָה סוֹפְרָן שֶׁל יִשְׂרָאֵל "הַלֵּוִי" שֶׁהָיָה מִשִּׁבְטוֹ שֶׁל לֵוִי. "לִפְנֵי הַמֶּלֶךְ וְהַשָּׂרִים", לִפְנֵי מֶלֶךְ מַלְכֵי הַמְּלָכִים הַקָּדוֹשׁ בָּרוּךְ הוּא וּבֵית דִּינוֹ. "וְצָדוֹק" זֶה אַהֲרֹן הַכֹּהֵן. "וַאֲחִימֶלֶךְ" שֶׁהָיָה אָחִיו שֶׁל מֶלֶךְ "בֶּן אֶבְיָתָר" בֵּן שֶׁוִּתֵּר הַקָּדוֹשׁ בָּרוּךְ הוּא עַל יָדוֹ מַעֲשֵׂה הָעֵגֶל, רַבִּי יְהוֹשֻׁעַ בֶּן קָרְחָה אוֹמֵר אַף לֵוִי הָיָה שְׁמוֹ עַל עִקַּר מִשְׁפַּחְתּוֹ. וּמֹשֶׁה, הֲרֵי עֲשָׂרָה אָמַר לוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא לְמֹשֶׁה חַיֶּיךָ מִכָּל שֵׁמוֹת שֶׁיֵּשׁ לְךָ אֵינִי קוֹרַאֲךָ אֶלָּא בְּשֵׁם שֶׁקְּרָאַתְךָ בַּתְיָה בַּת פַּרְעֹה, (שמות ב, י) "וַתִּקְרָא שְׁמוֹ מֹשֶׁה", הָוֵי וַיִּקְרָא אֶל מֹשֶׁה.