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 surnamesBalsama
The Balsam surname in historical dictionaries
Patronymica Britannica (1860)
BALSAM. From Balsham In Cambridgeshire, which Fuller characterizes as "an eminent village," and the only one in England bearing the name. The place was anciently called Bals-hani, not Balsh-am.