Hi, someone recently educated me on this name and thought it should be here for future readers. Eppa/Epa was apparently the shortened form of Epaphroditus (a man Paul writes about in Philippians, and a man credited as being the 'first bishop of Philippi' and a Catholic saint. Philippians 2:25, 2:30, and 4:18, states that he was an emissary from Philippi that was a great help to Paul.)
This name is used in a few early Virginia families, and was used in England as well during the same time period (as early as the early 1600's).
Eppy and Eppey were nicknames of Eppa/Epa.
Edited to add this link:http://www.terms.n2genealogy.com/nicknames.html