Possibly from a French place name or a short form of Laurence; also linked to a type of marble.
Rance carries a pleasingly layered etymology. Its most direct route runs through Old French rance, a word for bramble or thorny branch, lending it a wild, untamed quality that suits a given name with an outdoor, frontier feel. A secondary thread connects it to the medieval variant of Lance, itself derived from the Germanic Lanzo — a name rooted in the word for land or territory — which places Rance in the company of chivalric names associated with the Arthurian lance-bearing tradition.
There is also a Belgian marble called rance, a red and grey stone quarried near the town of Rance in Hainaut, beautiful enough that the stone appears in the Palace of Versailles. As an American given name, Rance found its most characteristic expression in the middle of the twentieth century, particularly in the South and Southwest, where monosyllabic names with a frontier resonance — Clint, Wade, Brett, Rance — enjoyed enduring favor. Rance Howard, the character actor and father of director Ron Howard, was perhaps its most publicly familiar bearer in Hollywood circles, giving the name a gentle association with the craft of performance.
The name also appeared in Western fiction and television as the kind of character who occupies a saloon doorway and speaks in measured sentences. Today Rance sits in rare but not extinct territory — recognizable enough not to require spelling aloud, distinctive enough to be noticed. It shares the quiet appeal of other short, sharp American masculine names that carry regional character without parochialism, and the bramble root gives it an unexpectedly wild botanical subtext for those who know it.