According to the Bible, when this Gileadite woman married, she retained her own name rather than take her husband's. In fact, he, (a priest no less) took her name instead. Who was this woman, and why is her title unusual?

He was no priest, but rather from the tribe of Judah, Hetzron. He took as a wife the sister of Gilead, Ya'ir (Jair) the "Gileadite", who had 23 farms (the farms of Ya'ir). (I Chronicles 2:21-22).

Elijah was also known as the "Gileadite" though he was from a town of priests (Teshev).

Nope, wrong person.

The dude I am referring to was a priest....

I looked at this question last night and came up with Barzillai, who in Ezra 2:61 married one of the daughters of Barzillai the Gileadite (a loyal follower of David) and "was called by their name."

The name apparently means "made of iron" in Hebrew, which is not mentioned on this particular site but can be found elsewhere.

http://www.christiananswers.net/dictionary/barzillai.html

Well I reckon that deserves a Golden Banana.

True, the answer I was looking for was that she was not known by any name, hence the unusual bit. Writers of the Bible obviously had their own reasons not to publish it. She is only referred to as "one of the daughters of Barzillai". I just thought it intriguing that a guy, way back then, would take his partners name.

The reference is (Neh.7:63).

By then, of course, the line was obscured. Barzilai the Gileadite was one of King David's companions some 400 years earlier. By Nehemiah's time Barzilai's family had grown into a rather large clan in its own right, as large as the tribe of Judah was in King David's day. A woman from that family would have been quite a good catch, hence her husband would have changed his name (unless he was from the royal family). (The name Barzilai does mean "from iron" as opposed to "the Brazilian")