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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The Horace surname in historical dictionaries
Patronymica Britannica (1860)
HORACE. I do not see why this name should not have been derived, through the French, from the Roman Horatius ; but Mr. Ferguson deduces it fi-om the 0. Saxon, Fi'iesic, and Norse, hros, Iwraz, hross, a horse.