A circle has a "name" and a "short name". The short name is used on the Org Chart to save space. These are modified in different ways.

A circle's name is modified through Governance in its supercircle. Go to the circle's supercircle, open a Governance Meeting, and choose Add/Edit Role. Find the circle whose name you want to change, and make the change there.
(Premium users may also use Asynchronous Governance Proposals to do the same thing.)

You can change the circle's "short name" by using the gear icon that appears after the circle's name on the circle page. The short name is the one that appears on the Org Chart. Only the Lead Link, Secretary, or your organization's GlassFrog Admins can do this. 

For the largest circle, which has no supercircle, the gear icon is where you change both the full name and the short name.