Likutei Moharan, Part II 66:3/ליקוטי מוהר"ן·תנינא ס״ו:ג׳

13. This is why people call the day after Yom Kippur “God’s Name.” This is because after Yom Kippur the concept of God’s Name is revealed. And this is why right after Yom Kippur they were commanded concerning Shabbat, because on the day after Yom Kippur God was reconciled with the Jewish people and cautioned them concerning the work of the Tabernacle. Then Moshe assembled them and cautioned them concerning Shabbat, so that they would not mistakenly say that the construction of the Tabernacle overrides Shabbat (as is brought in Rashi on Exodus 35:2). It follows, that immediately after Yom Kippur they were cautioned concerning Shabbat. And Shabbat is the Name of the Blessed Holy One (Zohar II, 88b), because then, after Yom Kippur, the concept of God’s Name is revealed.

2For when they punish a person, they uproot him from the source of his life-force. Thus, conceptually, even other punishments are called death, as it is written (Exodus 4:19), “for all the men seeking your life have died”—and our Sages, of blessed memory, taught: they became paupers (Avodah Zarah 5a). The name is the life-force, as in “a living soul is its name” (Genesis 2:19). And His name is associated with our name, as it were (Yerushalmi, Taanit 2:6). Therefore, whenever Israel suffers some punishment, God forbid, it harms the Blessed One Himself, as it were. This is because punishment primarily harms the life-force, which is the name—and His Name is associated with ours.

3And so, when Moshe said: “But if not, please wipe me out” (Exodus 32:32), God answered him: “He who has sinned against Me, I will wipe him out” (ibid. :33). Moshe requested that God do it for the sake of His Great Name, which is associated with our name. And since God’s Name is associated with ours, it follows that when He punishes them, He harms Himself, as it were. Therefore, our Sages, of blessed memory, taught: He does not rejoice… (Megillah 10b), because He harms Himself, as it were, for His Name is associated with our name.

4It follows, that when God was reconciled with the Jewish people on Yom Kippur and said “I have forgiven, according to your word,” then His Name, which is associated with our name, was exalted, as it were. Therefore, immediately after Yom Kippur they were commanded concerning Shabbat, as mentioned above. For Shabbat is the name of the Blessed Holy One, as mentioned above. And this is why the day after Yom Kippur is called “God’s Name.” As a result of the pardoning and forgiveness that is effected on Yom Kippur, God’s Name is exalted.