If you rename a taxonomy term in SharePoint, the change doesn’t take effect instantly.  You have to wait for the SharePoint Timer Job “Taxonomy Update Scheduler” to run, which by default is every 1 hour.

If you want the change to take place immediately, or to change the job schedule, open Central Administration -> Monitoring -> Review job definitions.  Scroll through the jobs until you reach the Taxonomy Update Schedule for the web application where you made the change.  Click on the job title and click Run Now, or reschedule the job.