Midras Keluaran 3:15: Shemot Rabbah, Ein Yaakov (Glick Edition), Otzar Midrashim & Kohelet Rabbah

“God said further to Moses: So shall you say to the children of Israel: The Lord, the God of your fathers, God of Abraham, God of Isaac, and God of Jacob, has sent me to you; this is My name forever, and this is My memorial for all generations” (Exodus 3:15).
“God said further to Moses: So shall you say to the children of Israel: The Lord [Y-H-V-H], the God of your fathers…” Go and speak to them in My name, which is the attribute of justice, with which I conduct Myself with them due to the merit of their forefathers. Know that I am speaking about the forefathers Abraham, Isaac, and Jacob; that is what is written: “The Lord, the God of your fathers, God of Abraham, God of Isaac, and God of Jacob, has sent me to you.” When Moses heard that He did not mention his father as He had initially,²⁰Exodus 3:6. See the midrash on that verse. he said before Him: ‘Master of the universe, are there sinners in the grave?’ He said to him: ‘No.’ He said before Him: ‘In the past, You said Your name in association with my father, and now You have removed it.’ He said to him: ‘Initially, I tempted you with inducements, from this point forward, I speak words of truth with you.’
“This is My name forever [leolam]” – [leolam is written] without a vav,²¹When spelled that way it evokes haalama, meaning concealment. so that a person will not enunciate God’s name, as it is written. “And this is My memorial for all generations” – so that one refers to Him only with an appellation.

Rabba b. b. Chana said in the name of R. Jochanan: "The sages are permitted to inform their disciples of the Tetragrammaton once in seven years, and according to others twice in seven years." R. Nachman b. Isaac said: "The opinion is more likely to be like those who say once in seven years, for it is written (Ex. 3, 15) This is My name forever (Le'olam); it is written le'alam, which means to be concealed." Raba wanted to lecture [concerning the explanation of God's name] from the pulpit, when a senior scholar warned him against it, saying: "Le'alam (to be concealed) is written." R. Abina raised the following contradiction: "It is written: This is My name Le'alam (to be concealed), and then it is written, This is My memorial, [showing that it should be read without concealing it]; i.e., thus said the Holy One, praised be He: 'Not as My name is written shall it be pronounced. It is written Yud, Hay, but is pronounced Alef, Daleth.'"

After that, entered ש and stood before the Holy Blessed One, and said before Him: "Master of the world! You should make Your world through me, for through me is called Your Explicit Name¹שמך beginning with a ש, as is written (Exodus 3:15) "This is My Name²שמי beginning with a ש forever, and also I am the first letter of the name Shaddai. The Holy Blessed One responded and said to it, "No." It said "why?" He said to it: "Since vanity³שוא beginning with a ש and falsehood⁴שקר beginning with a ש are both called by you, and falsehood has no legs just as you have no legs. How could I create the world on a letter with no legs?" Immediately it left from before His presence with a disappointed soul.