Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
We don't have any stats on how common this name is. This is probably because it's very rare in the UK.
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Related and similar surnamesSwayne
The Swain surname in historical dictionaries
Patronymica Britannica (1860)
B° SWAIN. The A-Sax. swcui, a pastoral servant, and the Scand. Sweyn, a proper name originally of the same import, have impressed themselves upon many localities, which in their turn have given designations to families. Among those which do not occur in gazetteers are Swainston, Swainsland (now Swaysland), Swanstou, and others.