This is from ultimaterollercoaster.com:
"The Traver Engineering Company erected both the Cyclone at Revere Beach, Massachusetts and the Thunderbolt at Savin Rock in Connecticut in 1925. These were Prior and Church designs and allowed Traver's company to cut their teeth building coasters. Both of these coasters were similar designs and typical Prior and Church rides.
One year later Traver premiered two coasters at the Philadelphia Sesquicentennial Exposition. The Cyclone was a wooden coaster with steel supports that had some of the same elements found on his later coasters, such as the spiraling drop, a sharp, downward helix, track made from eight layers of wood and articulated cars. This coaster is also the first coaster to use the name Cyclone, which would later become synonymous with powerful wooden roller coasters."
I don't know how reliable this information is. If it is correct, then the CI Cyclone is not the first to use the name. It's really hard to tell, as there is always conflicting information (dates, speed, height, etc.) about these old coasters.