Origin of the name Ollie:

Pet form of Oliver, a name derived from the French Olivier, which is generally considered to be from the Old French olivier (olive tree). Some believe it is of Germanic origin, however, and is thus probably from the Middle Low German Alfihar, a compound name composed of the elements alf (elf) and hari (army): hence, "elf army."

From A World of Baby Names by Teresa Norman.