Its source is Brandr, an Old Norse name meaning "Sword."
In modern English, we speak of a warrior ''brandishing'' his sword -- that is, swinging it in the air as a display of powerful swordsmanship. Both this word and the Old Norse source of Brenda share an ancestor with the English word ''brand,'' meaning to mark by burning.
Linguists theorize that the sight of a sword flashing in the sun gave the impression that it was on fire. This thrilling (or terrifying) sight may have inspired the Old Norse expressions that gave rise to the ancient name Brandr, the modern English word ''brandish,'' and ultimately the name Brenda.