Mr. Leo Garfinkel wrote:

Dear Rabbi,

What are the seven names of Mount Sinai and what do they mean?

Dear Mr. Leo Garfinkel,

According to the Midrash, Har Sinai has seven other names. All together it has eight names, as follows:

1. Har Sinai - from the word sneh - "bush." This refers to the burning bush on Har Sinai. Also, Sinai is related to the word sinah - "hatred" and "rejection." By giving the Torah to human beings instead of to the angels, G-d thereby rejected the angels.
2. Har Ha-Elokim - "G-d's Mountain," because G-d revealed His Torah there to the Jewish people. Through the Torah, the Jews become a G-dly people.
3. Beit Imi - "My Mother's House." By accepting the Torah the Jews were born as a nation.
4. Har Chorev, from the word "cherev" - "sword." The Torah invests special Torah courts, sanhedrin, with authority to try capital cases.
5. Har Chemed - "Desirable Mountain." G-d desired Mount Sinai as the place from which to give the most desirable of treasures, the Torah.
6. Har Bashan from the word "shen" - "tooth." Sustenance and blessing come to the world in the merit of Torah study and observance. Just as teeth prepare the food for digestion, so too the Torah brings nourishment to the world.
7. Har Gavnonim, from the word "gevina" - "cheese." Cheese is a metaphor for purity, probably because it's made from pure white milk.
8. Har Moriah - "Mountain of Teaching," where G-d taught Moses the Torah.

Sources:

• Shmot Rabbah 2
• Bamidbar Rabbah 1
• Shir Hashirim Rabbah 8