The Collaborative International Dictionary of English v.0.48:

Old Dominion \Old Dominion\
   Virginia; -- a name of uncertain origin, perh. from the old
   designation of the colony as "the Colony and Dominion of
   Virginia."
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

Old Dominion
    n 1: a state in the eastern United States; one of the original
         13 colonies; one of the Confederate States in the American
         Civil War [syn: Virginia, Old Dominion, Old Dominion
         State, VA]