Some call the eleventh of Tishre "b'shem Hashem" ("בשם ה׳"). (I assume this is a hasidic term, since, according to what I've heard, the name comes from the Baal Shem Tov.) Why is it called that?
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The various names of Hashem are means by which created beings relate to Him; His own Essence is beyond any names. Our sins cause a blemish in the name Havayah, and during the time of forgiveness of sins [Aseres Yemei Teshuvah, or maybe more broadly also including Elul] we rise up to the level of "before [i.e., above] Havayah." Thus, the day after Yom Kippur can't be associated with any specific divine name - it's just "Hashem's Name."
In a footnote there, the Rebbe points out that Eshel Avraham (Buczacz, Orach Chaim 624:5) gives a different reason, also in the name of the Baal Shem Tov: because on this day we once again begin mentioning Hashem's name where we had omitted it before, saying הא-ל הקדוש instead of המלך הקדוש.
He concludes that "these two explanations may be reconciled," but doesn't suggest how.