Edit a tag from the Tags page. When you edit a Tag, it will update with the new name for any person that it's been applied to.
To edit a tag:
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Click People > Tags
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Locate the Tag you want to edit
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Click Edit
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Edit the Tag name
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Click Update Tag
Changing the name of a Tag here will not change the Tag name in any automations or existing Liquid in emails; those will need to be updated manually.