The name Ben-hur in the Bible
Whether Ben-hur is a Biblical name has been disputed (because the man named Ben-hur might simply have been a "son of Hur", which is what Ben-hur means). But the Hebrew construct ben hur occurs in 1 Kings 4:8, where Ben-hur is mentioned among the twelve deputies of king Solomon of Israel. The only detail we know of this Ben-hur is that he was stationed in the region of Ephraim.
Etymology of the name Ben-hur
The name Ben-hur consists of two elements. The first part is the word בן (ben), generally meaning son:
The second part of the name Ben-hur is the same as the name Hur. The origin and meaning of the name Hur is not known for sure but that's not because there are no candidates: In fact, there are so many possibilities that we don't know which one is the right one:
The name Ben-hur may mea Son Of Hur, or it may mean One Of The Burnings/Nobles/Holes/Whites.
For a meaning of the name Hur, Jones' Dictionary of Old Testament Proper Names proposes Cavern. BDB Theological Dictionary says to have no clue, and NOBSE Study Bible Name List either takes the name Hur from another language, or bends the meaning of Noble or Freeman into Splendor.