Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
RAINY
As described in historical dictionaries
Patronymica Britannica (1860)
RAINY. R.VINEY. Fr. Re?2c, renatus, boru-again, has been suggested as a probable origin. See, however, Reynolds.