Couldn’t find much on the origin of the word ‘Rain’ but here is what I found. Kind of strange there isn’t much out there on the history of this word. Let me know if you find something more.
From Middle English reyn, rein, from Old English rēn, reġn (“rain”), from Proto-Germanic *regnaz (“rain”) (compare West Frisian rein, Dutch regen, German Regen, Danish and Norwegian regn), of uncertain origin. Possibly from pre-Germanic *Hréǵ-no-, from Proto-Indo-European *Hreǵ- (“to flow”) (compare Latin rigō (“wet, soak”), Lithuanian rõki (“drizzling rain”), Albanian rrjedh (“to flow, drip”)), although the consonant reflexes don’t match.
Old English regn “rain,” from Proto-Germanic *regna- (source also of Old Saxon regan, Old Frisian rein, Middle Dutch reghen, Dutch regen, German regen, Old Norse regn, Gothic rign “rain”), with no certain cognates outside Germanic, unless it is from a presumed PIE *reg- “moist, wet,” which may be the source of Latin rigare “to wet, moisten” (see irrigate). Rain dance is from 1867; rain date in listings for outdoor events is from 1948. To know enough to come in out of the rain (usually with a negative) is from 1590s. Rainshower is Old English renscur.
Old English regnian, usually contracted to rinan; see rain (n.), and compare Old Norse rigna, Swedish regna, Danish regne, Old High German reganon, German regnen, Gothic rignjan. Related: Rained; raining. Transferred and figurative use of other things that fall as rain (blessings, tears, etc.) is recorded from c. 1200.
To rain on (someone’s) parade is attested from 1941. Phrase to rain cats and dogs is attested from 1738 (variation rain dogs and polecats is from 1650s), of unknown origin, despite intense speculation. One of the less likely suggestions is pets sliding off sod roofs when the sod got too