[list=1][*] Click  move  at the top
[*] Fill in the new name
[*] Tell others why you're moving the page by filling out the "Reason:" field
[*] Click "Move". Done!
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Details:
[list][*] The Talk page will be automatically moved if it exists. Unless the destination had a talk page already, in which case you will have to move the content over manually.
[*] A redirect will automatically be created from the old name to the new name.
[*] The edit history of the page will follow to the new location
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[list][*] You might want to check if something links to the old location by using "What links here" and update the links to the new location. Especially if there's redirects to the old location; MediaWiki won't automatically follow double redirects.
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There are several reasons why you might wish to rename a page (one that you have found or created):
[list][*] The title has been misspelled.
[*] The title does not follow the wiki's naming conventions (such as BRWiki's Naming Policy).
[*] The scope of the article has been reduced, extended or otherwise changed.
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The terms "rename" and "move" mean the same in this context. They just refer to different models for picturing the operation:
[list][*]rename: keep the page but give it another name; the page history is now attached to the new name; a new page with the old name is created which redirects to the new name and which page history records the renaming.
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[list][*]move: move the contents and the page history to a new page; change the old page into a redirect; change the page history into one that only records the renaming.
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Since the system marks the page with the old name as new page, it applies the first of the two models. This model avoids "changing the history", a kind of "historical revisionism". An oddity is that the renaming itself, which can be considered an important event in the history of the page, is not recorded as such; it is recorded indirectly, namely in the history of the redirect page.

Note that you have to be logged in to rename a page this way; regarding the set preferences:
[list=1][*]there is no button for this in the nostalgia skin;
[*]the button is in the quickbar, so this must be on.
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With the correct page displayed, click on the "Move" tab near the top of the page. You'll be asked for a new name for the page, and given the option to also move the page's talk page. NOTE: Unless you know what you're doing, it's safest to say yes. Click the "move page" button and the page will be renamed to the new title. The old title will become a redirect page, so any links to the old title will still go to the new page. However, note that double redirects (pages that redirect to the original page), will not automatically follow to the new page, so you will have to refer them manually (as explained below)

The "move page" function keeps the entire edit history of the page, before and after the move, in one place, as if the page were always named that way. So, it's preferable to use this method over just cutting text out of one page and pasting it into a new one; old revisions, notes, and attributions are harder to keep track of it you do that. (But you may have to if, for instance, you're splitting a page into multiple topics. If you do, please include a note in the new pages's edit summary and talk page stating where you took the text from.)
The move itself is shown in the edit history of the page with the old title.

If the new title already exists but is just a redirect to the old title, with just one line in the page history, the creation of the redirect, then you can rename the page. The most common case in which this applies is that of re-renaming a page back to its original name. As mentioned, this works only if the redirect that was automatically created in the first renaming, has not been edited.
The result is that the history of the page is preserved (note that you may have to refresh the history page on your browser), but without any sign of the two moves. The edit history of the page with the intermediate title shows the latest move only. The information about the first move (including user name, date and time) is lost: it is no longer in any page history or on any watchlist or Related Changes page, and not even in User contributions; only if the first move has been recent enough, then it is still available in the Recent Changes; how long depends on the edit activity on the site; e.g. one may be able to retrieve the edit lines of the last 2000 edits, which may cover months or just a few hours. To avoid loss of information, copy the edit line concerned to one of the talk pages. This has to be done before the second move, using the page history of the page with the original name; if the second move is soon enough after the first move, it can also be done afterwards, using Recent Changes.
The information about the second move is more complete in the Recent Changes than in the edit history of the page with the intermediate title: it mentions "B moved to A over redirect".
More moves back and forth are possible, and always the page history of the current title does not show any moves, and that of the other title only contains the edit line of the latest move. There is no record at all of a "move war" (except again, on Recent Changes) unless documented on the talk pages.
Earlier there was a bug, which has been fixed but not retroactively, as follows:

If the new title already exists and isn't just a redirect to the old title, with no history, the wiki will tell you that you can't rename the page. You'll either have to manually merge the two pages together, or -- only if there's no real content in the page -- ask an Administrator to have it deleted or list it on your project's "votes for deletion" page in order to make room for moving the page.
Another thing to remember is that redirects to redirects aren't automatically followed (this prevents infinite loops and spaghetti linking). Always check the What links here for your page, and if there are multiple levels of redirects, go fix the links to point to the new location directly. But this can be troublesome because your new moving might be reverted soon. Take some time to make sure there is no objection to your moving.
Avoid moving a page while the edit box of the corresponding Talk page is open: when you hit "Save page" you overwrite the redirect to the new talk page (you do not get the usual warning that the page has been edited while your edit box was open) and get a duplication of the contents of the talk page, with your latest addition added to the old instead of the new one.
It is useful to copy the message "Page ... moved to ..." to the new talk page, especially if there has been discussion about the name of the page.

Normally, to undo a move from page A to page B, simply:
[list=1][*] move page B back to page A
[*] list page B (now a history-free redirect) on your project's "votes for deletion" page, or (Admins only) just delete it.
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However, if page A has subsequently been edited, or the move software is behaving weirdly, only an Admin can sort things out:
[list=1][*] delete page A (make sure it has no useful history - you may wish to add an explicit author credit on a talk page to compensate)
[*] move page B to page A.
[*] delete page B (should be a history-free redirect to page A)
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"Move wars" are highly unproductive, and leave vast numbers of pointless redirects littering the place, which some poor soul will have to fix.

To swap pages A and B, including history:
[list=1][*] Move page A to page C (previously non-existing)
[*] list A on votes for deletion, or (Admins only) just delete it.
[*] Move page B to page A (allowed because A is deleted)
[*] delete B as above
[*] Move page C to page B (allowed because B is deleted)
[*] delete C as above
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Many past renamings took place before the move page function was created by our hard-working developers, and others are done by people not aware of this function. Such manual moves were done using cut and paste As a result, the page history of an article or talk page can be split among two or more different pages.
In some circumstances, Administrators are able to fix this by merging page histories.
Warning: this procedure may only be undone by a developer, spending quite silly amounts of time: to undo a merge, every single version has to be manually reassigned to the correct source page. Do not do this if you're not sure what you're doing.
Follow this procedure to merge page histories:
[list=1][*] suppose we wish to merge edit history from Alabama/History (old title) into History of Alabama (new title):
[*] Delete History of Alabama, with comment deleting to merge page histories - back soon.
[*] Move Alabama/History to History of Alabama, using the move tool.
[*] undelete the History of Alabama article.
[*] Edit History of Alabama to restore the most recent version.
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