Firstly: Names for Muzadlifah
The root word zalafa means to draw close to something. Muzdalifah is an area in Mecca.
Why it was named Muzdalifah
a. Because they approach Mina while there, and izdilaf means getting close.
b. Because people gather there, and izdilaf means gathering.
2. The Sacred Monument
Allah named Muzdalifah the Sacred Monument (al-Mash`ar al-Haram). Allah the Exalted says: “But, when you press on in the multitude from `Arafat, remember Allah by the sacred monument. Remember Him as He has guided you, although before you were of those astray.” (Al-Baqarah: 198)
The Sacred Monument mentioned in the Qur’an is all of Muzdalifah. This is the position of the majority of Qur’anic exegetes and people of hadith and Prophetic biography (seerah).
The Messenger of Allah ﷺ referred to Muzdalifah as Jam`.
The reason it was named Jam`
It was named Jam` literally: combining because of the two prayers combined there. Some hold that it was described as such because they gather there and draw closer to Allah; i.e. through standing there.
Secondly: Boundaries of Muzdalifah
The boundaries of Muzdalifah are between the two narrow paths  The narrow paths are two mountainous paths: one between Jam` and `Arafah and the other between Mecca and Mina. and Wadi Muhassir. The boundaries are not part of it. Spending the night at Muzdalifah is effected by being present in any portion of it.