The name Rotary was chosen to reflect the custom, in the early days of the first Rotary Club in Chicago, of rotating the site of club meetings among the members' places of business. This rotation, an integral part of the founder's original concept, was designed to acquaint members with one another's vocations and to promote business, but the club's rapid growth soon made the custom impractical.

The Rotary emblem

Rotary's first emblem was a simple wagon wheel (in motion with dust) representing civilization and movement. It was designed in 1905 by Montague Bear, a member of the Chicago club, who was an engraver, and many Rotary clubs of the time adopted the wheel in one form or another.

In 1922, authority was given to create and preserve an official emblem, and the following year the present gear wheel with 24 cogs and six spokes was adopted. A keyway was added to signify that the wheel was a "worker and not an idler." At the RI Convention in 1929, royal blue and gold were chosen as the official colors.

Here is a link to a history of the Rotary Wheel.