Yes, taxi beat is super popular in Greece. Essentially its just like uber but it uses all of the existing taxi drivers in GreeceI have never used ride share in Greece, and I am not sure that people really do that. I tend to use taxis, public transport, my legs, or rent a car.
According to this tripadvisor thread, there is an app that Greeks use that can help you secure a taxi called Taxibeat. I have never used it. Has anyone heard of it?