Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
EAGAR
As described 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.