The term Olive Ash does not refer to any specific species of Ash (Fraxinus genus), but instead is in reference to the darker, streaked heartwood found in some Ash trees, which tends to resemble the wood of Olive trees in the Olea genus. And it should come as little surprise that Olive Ash can be a dead ringer for actual Olive (with the exception of the porous grain structure, which gives its true identity away easily), because both Ash and Olive are placed in the same family: Oleaceae.
The dark-on-light stripes of Olive Ash are also vaguely reminiscent of Zebrawood; though interestingly enough, the darker portions of Olive Ash do not correspond to the growth rings on the tree, but are independent of them, as can be observed from the endgrain scan seen below.
Olive Ash is a sought-after veneer, as well as desired for turning blanks. Olive Ash burl in particular is a highly valued veneer for its unique colors and swirly grain patterns. Far and away, most commercial Olive Ash occurs as European Ash (Fraxinus excelsior) and is typically imported from Europe.
Scans/Pictures: A special thanks to Steve Earis for providing the wood sample and turned photo of this wood species.