🔼The name Midian in the Bible
Midian is a son of Abraham with Keturah (Genesis 25:2). One of his five brothers is called Medan, which differs from Midian only slightly. They lived in Arabia but maintained a lively international trade, which is how Midianite (מדינים) traders could transport Joseph from Canaan to Egypt (Genesis 37:28) and sell him to Potiphar (Genesis 37:36, now spelled מדנים).
Four centuries later Moses fled from Egypt to the land of Midian (Exodus 2:15). There he met Jethro, the priest of Midian, and married his daughter Zipporah. Stephen commemorated this event in his sermon to the council (Acts 7:29, spelled Μαδιαν, Madian).
Jethro appears to have been instrumental in creating the organizational structure of Israel (Exodus 18:17), but Moses did not remain kindly inclined to the people of his wife. When Israel was on the move, the leaders of Moab and Midian feared that they would destroy their lands by simply walking through them, and so they summoned Balaam to curse Israel. That didn't go the way they had hoped, but the enmity between Israel and Midian was set and wouldn't abate. YHWH instructed Moses to take full vengeance on the Midianite (מדיני), and Israel killed every male and non-virgin female Midianite they could find, including the five kings and Balaam the prophet (Numbers 31:1-18).
By the time of the judges, the Midianites had managed to recuperate and were able to subdue the Israelites. But after seven years, the Lord raised up Gideon, son of Joash the Abiezrite, who engaged the Midianites and smote them with a band of 300 men (Judges 6). After that, the Midianites disappear entirely from the Biblical stage.
🔼Etymology of the name Midian
The name Midian appears to be derived from the noun מדון (madon), meaning strife, derived of the Hebrew verb דין (din), meaning to judge or plead:
The word מדין occurs in Judges 5:10 with an unclear meaning: "rich carpets" according to NAS and JSP and "judgment" according to the KJV.
In 2 Samuel 21:20 our word means war or battle, and in Proverbs 19:13, the constant dripping of a 'contentious' wife could equally well read a Midianite wife (מדיני). That is to say: not literally a Midianite wife but rather a wife like a Midianite.
The proper plural, מדינים, or Midianites, occurs with the meaning of 'contentions' in Proverbs 18:18, and the to-be-avoided 'woman of contentions' or a 'woman like a bunch of Midianites' in Proverbs 21:9.
🔼Midian and Medina
Whether the name Midian is related to the name of the famous Arabic city of Medina — where Muhammad is buried and which is called Yathrib in the Quran — is not clear, although the short answer is no. The name Medina, namely, comes from the word madina meaning city.
However, the word madina is just one of a few words for city. This word madina appears to only denote a specific kind of walled city and the word also appears to have been imported from Ugaritic, where it denotes an assembly of deities within an enclosure. These deities probably behaved like all assembles, whether divine or not, which is debate and decree. So the slightly longer answer is yes.
The name Midian means Strife (Jones' Dictionary of Old Testament Proper Names) or Place Of Judgment (NOBSE Study Bible Name List).