Unless you are a project administrator you can only rename templates that were created by you. Read more.
Open "Manage Templates" dialog:or "Checklist Templates" page:
Most of the screenshots below were taken from inside Manage Templates dialog but the process is identical on Checklist Templates page.
New dialog pops up. Enter a new name for the template and click "Rename":
Template name must be unique (it is not possible to have more than one template with a given name).