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 surnames
The Dames surname in historical dictionaries
Patronymica Britannica (1860)
DAMES. 1. Perhaps the same as Ames with the local prefix D'. 2. Perhaps an old personal name. Dame without prefix is found in H.R.