The Shechina appeared to Moses for the first time at the burning bush event as an angel.
“וַיֵּרָא מַלְאַךְ יְהֹוָה אֵלָיו בְּלַבַּת אֵשׁ מִתּוֹךְ הַסְּנֶה וַיַּרְא וְהִנֵּה הַסְּנֶה בֹּעֵר בָּאֵשׁ וְהַסְּנֶה אֵינֶנּוּ אֻכָּל”
“And the angel of YHVH appeared to him in a flame of fire out of the midst of a bush. He looked, and behold, the bush was burning, yet it was not consumed.”
For Jacob the Shechinah appeared in the image of Rachel because she’s the aspect of Malchut.
“וַיֹּאמֶר לָהֶם, הֲשָׁלוֹם לוֹ; וַיֹּאמְרוּ שָׁלוֹם–וְהִנֵּה רָחֵל בִּתּוֹ, בָּאָה עִם-הַצֹּאן”
“And he said to them, “Is it well with him?” And they said, “It is well, and here is Rachel his daughter coming with the sheep.””
Abraham had a different revelation.
“וַיֵּרָא אֵלָיו יְהוָה, בְּאֵלֹנֵי מַמְרֵא; וְהוּא יֹשֵׁב פֶּתַח-הָאֹהֶל, כְּחֹם הַיּוֹם”
“Now YHVH appeared to him (Abraham) by the oaks of Mamre, while he was sitting at the tent door in the heat of the day.”
The Zohar compares the three and says that it looks like Abraham received the higher type of revelation of the Shechina because the name YHVH appeared to him.
“וָאֵרָא, אֶל-אַבְרָהָם אֶל-יִצְחָק וְאֶל-יַעֲקֹב–בְּאֵל שַׁדָּי; וּשְׁמִי יְהוָה, לֹא נוֹדַעְתִּי לָהֶם”
“and I appeared to Abraham, Isaac, and Jacob, as God Almighty, but by My name, YHVH, I did not make Myself known to them.”
This verse said by God to Moses testifies that God didn’t appear to the patriarch through the name YHVH. The Zohar explains that the Shechina appeared to Abraham as the name ADNY that is the name we use in the level of Malchut instead of YHVH. Because Moses is on the level of Da’at, which is above Zeir Anpin, the Shechina could reveal itself to him as a unification with the upper levels and the name YHVH.