Yom Kippur: Why is it Called God’s Name Day

Yom Kippur is sometimes called Gottes Namen, God’s Name, Day. Some of the reasons offered for this name are:
1 -The Kohen Gadol pronounced the shem ha-meforash as part of the avodah
2 - We conclude with yichud Hashem reciting Hashem hu ha’Elokim, seven times.

Rav Dovid Cohen offered another explanation. The Ramban says the Bnei Yisrael lost knowledge of the Names, shemos, of Hashem at the chet ha-‘egel, the sin of the Golden Calf. At mattan Torah God provided them with weapons i.e. shemos to protect themselves against pestilence and the angel of death. Death would have been conquered as in the time of Adam before he sinned in the Garden of Eden when there was no death.

Va’yis’natzlu v’nei Yisrael es ‘ed’yam mei’har choreiv.
And the people of Israel stripped themselves of their ornaments by the mount Horeb (Shemos 33:6)

The Ramban on this pasuk is based on the Midrash:
R. Simeon b. Yohai said: [They stripped themselves of] the belts with which He had girded them (Shemos Rabbah 45:2).

BEHOLD, I SEND AN ANGEL BEFORE THEE (XXIII, 20). Thus it is written, I said: Ye are godlike beings (Ps. LXXXII, 6). Had Israel waited for Moses and not perpetrated that act, there would have been no exile, neither would the Angel of Death have had any power over them. And thus it says, And the writing was the writing of God, graven (haruth) upon the tables (Ex. XXXII, 16). What is the meaning of ’haruth’? R. Judah and R. Nehemiah each explained it. R. Judah says: Free (heruth) from captivity; and R. Nehemiah says: Free from the Angel of Death. When Israel exclaimed: ’All that the Lord hath spoken will we do, and hearken’ (ib. XXIV, 7), the Holy One, blessed be He, said: ' If I gave but one commandment to Adam, that he might fulfill it, and I made him equal to the ministering angels,- for it says, Behold, the man was as one of us (Gen. III, 22) --how much more so should those who practise and fulfill all the six hundred and thirteen commandments-not to mention their general principles, details, and minutiae-- be deserving of eternal life?’ This is the meaning of And from Mattanah to Nahaliel--nahalu (Num. XXI, 19)4; for they had inherited [through the Torah, given as a gift], from God eternal life. As soon, however, as they said, ’This is thy god, O Israel’ (Ex. XXXII, 4), death came upon them. God said: ‘You have followed the course of Adam who did not withstand his trials for more than three hours, and at nine hours death was decreed upon him. “ I said: Ye are godlike beings,” but since you have followed the footsteps of Adam, Nevertheless ye shall die like men. (Shemos Rabbah 32:1)

The Ramban says, that Yisrael accepted death upon themselves as punishment in repentance and remorse for their sin with the Golden Calf.

Yisrael’s voluntary acceptance of death by giving up the power of the shemos to protect them was part of their teshuvah. The second luchos given on Yom Kippur is a sign that their teshuvah was accepted. Hence, the connection to Yom Kippur and the shemos of Hashem on God’s Name Day – Gottes Namen.