(א) וַיֵּ֥לֶךְ אִ֖ישׁ מִבֵּ֣ית לֵוִ֑י וַיִּקַּ֖ח אֶת־בַּת־לֵוִֽי׃ (ב) וַתַּ֥הַר הָאִשָּׁ֖ה וַתֵּ֣לֶד בֵּ֑ן וַתֵּ֤רֶא אֹתוֹ֙ כִּי־ט֣וֹב ה֔וּא וַֽתִּצְפְּנֵ֖הוּ שְׁלֹשָׁ֥ה יְרָחִֽים׃ (ג) וְלֹא־יָכְלָ֣ה עוֹד֮ הַצְּפִינוֹ֒ וַתִּֽקַּֽח־לוֹ֙ תֵּ֣בַת גֹּ֔מֶא וַתַּחְמְרָ֥הֿ בַחֵמָ֖ר וּבַזָּ֑פֶת וַתָּ֤שֶׂם בָּהּ֙ אֶת־הַיֶּ֔לֶד וַתָּ֥שֶׂם בַּסּ֖וּף עַל־שְׂפַ֥ת הַיְאֹֽר׃ (ד) וַתֵּתַצַּ֥ב אֲחֹת֖וֹ מֵרָחֹ֑ק לְדֵעָ֕ה מַה־יֵּעָשֶׂ֖ה לֽוֹ׃ (ה) וַתֵּ֤רֶד בַּת־פַּרְעֹה֙ לִרְחֹ֣ץ עַל־הַיְאֹ֔ר וְנַעֲרֹתֶ֥יהָ הֹלְכֹ֖ת עַל־יַ֣ד הַיְאֹ֑ר וַתֵּ֤רֶא אֶת־הַתֵּבָה֙ בְּת֣וֹךְ הַסּ֔וּף וַתִּשְׁלַ֥ח אֶת־אֲמָתָ֖הּ וַתִּקָּחֶֽהָ׃ (ו) וַתִּפְתַּח֙ וַתִּרְאֵ֣הוּ אֶת־הַיֶּ֔לֶד וְהִנֵּה־נַ֖עַר בֹּכֶ֑ה וַתַּחְמֹ֣ל עָלָ֔יו וַתֹּ֕אמֶר מִיַּלְדֵ֥י הָֽעִבְרִ֖ים זֶֽה׃ (ז) וַתֹּ֣אמֶר אֲחֹתוֹ֮ אֶל־בַּת־פַּרְעֹה֒ הַאֵלֵ֗ךְ וְקָרָ֤אתִי לָךְ֙ אִשָּׁ֣ה מֵינֶ֔קֶת מִ֖ן הָעִבְרִיֹּ֑ת וְתֵינִ֥ק לָ֖ךְ אֶת־הַיָּֽלֶד׃ (ח) וַתֹּֽאמֶר־לָ֥הּ בַּת־פַּרְעֹ֖ה לֵ֑כִי וַתֵּ֙לֶךְ֙ הָֽעַלְמָ֔ה וַתִּקְרָ֖א אֶת־אֵ֥ם הַיָּֽלֶד׃ (ט) וַתֹּ֧אמֶר לָ֣הּ בַּת־פַּרְעֹ֗ה הֵילִ֜יכִי אֶת־הַיֶּ֤לֶד הַזֶּה֙ וְהֵינִקִ֣הוּ לִ֔י וַאֲנִ֖י אֶתֵּ֣ן אֶת־שְׂכָרֵ֑ךְ וַתִּקַּ֧ח הָאִשָּׁ֛ה הַיֶּ֖לֶד וַתְּנִיקֵֽהוּ׃ (י) וַיִּגְדַּ֣ל הַיֶּ֗לֶד וַתְּבִאֵ֙הוּ֙ לְבַת־פַּרְעֹ֔ה וַֽיְהִי־לָ֖הּ לְבֵ֑ן וַתִּקְרָ֤א שְׁמוֹ֙ מֹשֶׁ֔ה וַתֹּ֕אמֶר כִּ֥י מִן־הַמַּ֖יִם מְשִׁיתִֽהוּ׃
משה is related to:
מצה (to pull something out of the water with big effort)
and
משח (to separate artificial from a fluid)
She didn't name him משוי (to Pull him out of the water)
instead, she named him משה (to rescue him from the water)
This may indicate the whole direction of education that Pharo's daughter wanted for her adoptive son as well as shaped his character from an early age.
With the name she tells him:
He should not forget his entire life that he was thrown into the water and that she rescued him. – Therefore he should have a soft heart and should always be ready to become a helper out of need, a מֹשֶה.
The Hebrew name should help to remind him of his origin. Pharo's daughter most definitely asked his mother how to say it in Hebrew otherwise she would have used the Egyptian version.
In this, the nobility of Moshe's saviour is expressed.
From this we can learn how important and defining every ones name can be.