Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
EASTGATE
As described in historical dictionaries
Patronymica Britannica (1860)
EASTGATE. From residence near the eastern gate of a towrr. The medieval form would be " Atte, de, or in, Estgate." Northgate, Westgate, and Southgate, well-luiown surnames, originated in like manner from the contiguity of the bearers' residences to the res23ective gates.