🔼The name Olivet in the Bible
Technically, the name Olivet occurs only once in the Bible, namely in Acts 1:12, which speaks of the mount (ορος, oros) named Ελαιωνος (Elaionos). Most other references to the famous Mount of the Olives in the New Testament speak of ορος των ελαιων (oros ton elaion; Matthew 21:1, 24:3, 26:30, Mark 11:1, 13:3, 14:26, Luke 19:37, 22:39, John 8:1), which means precisely that (Luke 19:29 and 21:37 have "the mount called ελαιων (of olives)").
The name Olivet belongs to the middle of three peaks of a ridge on the east side of Jerusalem, flanking the valley of Jehoshaphat, which is part of the Kidron valley. The peak to its north was called Scopus (not mentioned in the Bible) and the one to its south bore the ominous name of Mount Mashkit or Mount of Corruption due to the pagan shrines and idols which Solomon placed there (2 Kings 23:13).
Olivet was not only covered with eponymous olive groves but also with an enormous grave yard, namely the Silwan Necropolis, which originated in the time of the early kingdom, possibly in the time of Solomon, and which today contains about 150,000 graves, including those of the prophets Haggai, Zechariah and Malachi (or so tradition demands). Olivet is about 80 meters higher than the temple mount, and allows a compelling bird's eye view of the city (the famous image of Jerusalem with the Dome of the Rock just within the wall in the foreground is from Olivet). From the time of the second temple, the new moon was announced from Olivet (Numbers 10:10, Psalm 81:3).
The gospel of Luke tells us that Jesus customarily went to the Mount of Olives (Luke 22:39) and even lodged there (21:37), which demonstrates that besides olive groves and a necropolis, Olivet also had towns for living people — Bethany, the hometown of Lazarus, being the most noted one. Since Jesus was arrested in the garden of Gethsemane, which was situated on Olivet, His passion technically began on the Mount of Olives. He also appears to have ascended into heaven from the Mount of Olives, since His disciples returned from it to Jerusalem after the event (Acts 1:12). And that makes Olivet a very special place indeed.
🔼The name Olivet in the Old Testament
We hear first of the Mount of Olives (in Hebrew: זית, zayit) when, fleeing from his rebellious son Absalom, king David ascended the mountain in tears and parted with the Ark of the Covenant (2 Samuel 15:30). We also learn that at its summit God was worshipped (15:32) but how that exactly worked isn't explained.
Strikingly, at some point during his temple vision the prophet Ezekiel witnessed the "glory of the Lord" depart from Jerusalem and settle on the eastern hill (Ezekiel 11:23, also see Ezekiel 1:28, 3:12, 10:4). This term "glory of the Lord" refers to the material manifestation in which He resides, and is mostly associated with the Shekinah, or the cloud that rested upon and within the tabernacle and temple (Exodus 40:34-35, Numbers 14:10, 1 Kings 8:11).
The prophet Zechariah too experienced a vision concerning the Mount of Olives, and he tells of how during the final battle, YHWH will stand on Olivet and split it from east to west, leaving a valley up to a mysterious place called Azel (Zechariah 14:4). How this vision translates in real-world terms isn't clear, or at least much debated, but it helped establish Silwan Necropolis as the front row seat for the eschatologically inclined.
🔼Etymology of the name Olivet
The name Olivet, that is to say: the Greek name Elaionos, comes from the noun ελαια (elaia), meaning olive (tree):
The name Elaionos means Place Of Olives or Olive Grove.