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 Eagar surname in historical dictionaries
Patronymica Britannica (1860)
EAGER. EAGAR. A trait of character ; or, perhaps, a corruption of Edgar (spelt in A-Sax. Eadgar) by the suppression of the letter D.