I was studying today parashat ha shavua (Devorim) and it is written there that Jews went from the Mountain of Chorev. Why is not called Sinai? What significance lies behind this name?
See Talmud Bavli Shabbat 89:
מדבר סיני שירדה שנאה לעכו"ם עליו ומה שמו חורב שמו ופליגא דר' אבהו דא"ר אבהו הר סיני שמו ולמה נקרא הר חורב שירדה חורבה לעכו"ם עליו
[Why was it called] the Wilderness of Sinai, because hostility [sin'ah] toward idolaters descended thereon. Whilst what was its [real] name? Its name was Horeb. Now they disagree with R. Abbahu, For R. Abbahu said: its name was Mount Sinai, and why was it called Mount Horeb? Because desolation [hurbah] to idolaters descended thereon. (translation based on Soncino)