You will have to remove the labels from all Issues:
https://confluence.atlassian.com/display/JIRAKB/How+to+Delete+Labels+in+JIRA
But if you do this by Bulk Editing, all other labels of the edited Issues will be removed.
A second way is to remove them directly in your DB, but this is just recommended if you really know what you are doing.
This might help:
https://answers.atlassian.com/questions/141323/is-it-possible-to-rename-a-label
I want to point-out that with a recent version of JIRA you can now remove a single label from issues using a bulk operation.
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If you have a large number of labels, removing from each issue will be impossible.
For that use case, we have developed an app: Label Manager for Jira Cloud
It allows managing labels (searching, filtering, changing name, deleting etc.) from a single page. Try it out and let us know if you face any issues.
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