Gathering for Heaven draws Torah down

ושם עצרת ע"ש הכנופיא דכ' הקהל לי את העם ואשמיעם את דברי.

And the name "Atzeres" is on account of the gathering, as it is written, "Assemble the people to Me, and I will let them hear My words."

The Sefas Emes explains "Atzeres" as a term of assembly (kenufya), rooted in Hashem's command to gather the people at Sinai so they could hear His words.

לי לשמי.

"To Me" — for My sake.

The word "to Me" stresses that this gathering was specifically lishmah, for the sake of Hashem's Name.

והוא כניסי' לשם שמים שמתאספין בני ישראל לשם שמים כדי שירד להם התורה מן השמים כדכתיב הבונה בשמים מעלותיו כשאגודתו על ארץ.

And this is a gathering for the sake of Heaven, that Bnei Yisrael assemble l'shem Shomayim so that the Torah should descend to them from the heavens, as it is written, "He who builds His upper chambers in the heavens, and founds His bundle (agudaso) upon the earth."

When Yisrael gather purely for Heaven's sake, they form an agudah on earth that draws the Torah down from above. The pasuk in Amos teaches that Hashem's "upper chambers" in heaven connect to the world precisely when His "bundle" — the united people — stands firm on the earth.

וכמו שהי' אז בפועל ממש שירד להם התורה מן השמים והוא ללמד על כל הדורות כשהכניסי' לשם שמים.

And just as it was then in actual fact, that the Torah descended to them from the heavens, so it teaches for all generations — when the gathering is for the sake of Heaven.

The literal descent of Torah at Sinai sets a pattern for all time: whenever Jews assemble l'shem Shomayim, that same drawing-down of Torah from above can recur.

וזה הכינוס שנעשה אז בזה היום נשאר לדורות מורשה קהלת יעקב לכן נקרא עצרת:

And this gathering that was made then on this day remained for the generations — "an inheritance for the congregation of Yaakov" — therefore it is called "Atzeres."

The assembly at Sinai on this day became a permanent inheritance, "morashah kehillas Yaakov"; because Atzeres is essentially this enduring sacred gathering, that is its very name.

Summary: "Atzeres" denotes the gathering of Bnei Yisrael at Sinai l'shem Shomayim. When the people unite purely for Heaven's sake, they form an agudah on earth that draws the Torah down from the heavens — as happened literally at Matan Torah. That sacred assembly became a lasting inheritance for all generations, "morashah kehillas Yaakov," and from it the festival takes its name.