No sir, the rename operation will not duplicate the category. They are both technically merge operations , just have different functions since a literal rename is not possible.
Rename = Moves all profiles to the final category and deletes the wrong category (the one which the rename template is on). The final category has to exist for this to work correctly.
Merge = Moves all profiles and tries to combine the text of the category to the final category. This is good when the original category has text content on it, but the new one does not. However, this operation requires a manual intervention by other members.