Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
WRENN
As described in historical dictionaries
Patronymica Britannica (1860)
WREN. WRENN. Not so likely from the bird as from the town of Rennes in Brittany. In H.R., however, it is Wrenne.
Origin: English
Region of origin: British Isles
Country of origin: England
Religion of origin: Christian
Language of origin: English