Revealing one of the Torah mysteries, the Arizal says in his writings that the four days between Yom Kippur and Sukkot correspond to the four letters of haShem’s Ineffable Name. According to an old Chassidic tradition, mentioned by the Baal Shem Tov, the day after Yom Kippur has a special name – “The Day of Shem haShem”.
The Day of Shem Hashem
On Yom Kippur, we access and reveal the very essence of our soul, which is one with the very essence of HaShem. Thus the day after Yom Kippur carries the designation “Shem Hashem”.
It is customary to start constructing (or at least planning) the sukkah immediately after Yom Kippur. Kitzur Shulchan Aruch: “People who are meticulous in observing the mitzvos begin to build the sukkah, immediately after the end of Yom Kippur, fulfilling the verse, “They go from strength to strength” (Psalms 84:8)”.
The Midrash (Vayikra Rabbah 30:7) describes the four days between Yom Kippur and Sukkot as a time when the Jewish people are “preoccupied with mitzvot… this one is occupied with his sukkah, this one is occupied with his lulav…”