Good question. Here's a little info that I dug up:
The origin of the verb 'taxi' came from the German word 'taxameter', first used in 1890. In 1907, England used the word 'taximeter' which was a method to compute the cab fare (which in both cases, defined the 'tax' to be charged) for the use of of a carriage, using time and distance. In 1911, the shortened word 'taxi' was used to define the slow movement of an airplane on land or water, such as to 'taxi' to the takeoff position, etc.
(Incidentally, note the use of the expression 'hover taxiing', regarding helicopters, in the Wikipedia article. Back in my day, we called it 'air taxiing', i.g., 'air taxi to the ramp'. IMO, neither term is correct. By definition, You can't taxi while airborne, not can you be moving laterally while hovering. Oh well).
73s