There are several reasons why you might wish to rename a<unk> (one that you have found or created):
The title has been misspelled.
The title does not follow the wiki's naming conventions
The scope of the article has been reduced, extended or otherwise changed.
The terms "rename" and "move" mean the same in this context. They just refer to different models for picturing the operation:
rename: keep the<unk> but give it another name; the<unk> history is now attached to the new name; a new<unk> with the old name is created which redirects to the new name and whose<unk> history records the renaming.
move: move the contents and the<unk> history to a new<unk>  change the old<unk> into a redirect; change the<unk> history into one that only records the renaming.
Since the system marks the<unk> with the old name as new<unk>  it applies the first of the two models. This model avoids "changing the history", a kind of "historical revisionism". The move is shown in the history of the<unk> (i.e. under the new name), although, oddly, the supplied reason of the move is only shown in the history under the old<unk> name.
Even though the<unk>  in all namespaces have a "move" link, a<unk> can not be moved if it is in the image or category namespace. To change the name of an image, one needs to upload it again, and copy the image description. To change the name of a category, one needs to change all category tags, and copy the editable part.
Moving pages
Watching pages
Face time
Reviewing grammar and punctuation
Itch differential diagnosis
How to create a  page
Page name
Nightmare