White most often began as an English nickname for someone fair-haired, pale, or known for white clothing—the bright counterpart to Brown. Color nicknames were practical tags in crowded parishes, and they became hereditary without pointing to one ancestral cottage.
Separately, some Scottish and Irish families ended up with White when Gaelic surnames meaning roughly “fair” or similar ideas were translated or anglicized into English. Those are different roots wearing the same English word. For a family page, lead with the English nickname, then note that Irish or Scottish lines may have a translated Gaelic story instead. Either way, it is descriptive, not a trade.