To rename a page in a wiki, it's called moving the page.
First of all, don't go moving other people's pages without "talking" to them first. Go to the page you want to move, click "discussion", then click "edit", and then write what you want to do. Watch the page, and see if you get an answer within, say, a week. If you don't get an answer, then seek help from a sysop, but don't move the page. (It's reasonable to put a link on that page to yours, though. See Help:Naming.)
To move one of your own pages to a new name, go to the page, and click "move". Pick a new name, and you're nearly done. In fact, you could just quit at this point, but if you want to be thorough, you should fix any links.
Behind the scenes, the wiki created a "redirect" for you, which is a special kind of page with the old name that redirects any browsers to your new, renamed, page. That way, your wikilinks will keep working just as they always did. But, for various reasons, you can't always rely on redirects. For one thing, they only work once. If the page is ever renamed again (or if it was renamed in the past) then you may have a 'double redirect" which doesn't work as well as you might expect. For another, someone might want to use the old page name as a "disambiguation page". That is, if you renamed a general page like "marathon" to a more specific name, like "HDR marathon", then someone else who wants to make a marathon page might see your redirect, and turn it into a page that explains to the readers what all the marathon pages are about. This is a good thing, because it helps the general wiki-reading public; however, it will make it less convenient for your readers to navigate your little corner of the wiki.
To fix links after moving a page, here's what you need to do. Go to the new page, and click "What links here". This will give you a list of all the pages that link to the new file. Probably just the automatically generated redirect will link to your page, but you will also see all the pages that link through that redirect. Go to each page, and turn the link into a "piped link" to your new page.
For example, if you moved "marathon" to "HDR marathon", then you may see that the "HDR" page has a link to "marathon" that you need to fix.
- Old link: We provide excellent [[marathon]] training.
- New link: We provide excellent [[HDR marathon|marathon]] training.
This is called a "piped link" because it uses the pipe character (vertical bar) to render the exact same text, "marathon" for the new link (HDR marathon) as it did for the old link (marathon).