Manual:$wgCookiePath

Cookies: $wgCookiePath
Explicitly declared "path" for cookies at the cookie domain
Introduced in version:Before 1.1.0
Removed in version:Still in use
Allowed values:(relative path)
Default value:'/'

Details

If you do not want your login to be persistent across Wikis running on the same server, and your installations all use the same database, you will need to modify the LocalSettings.php file

$wgCookiePath = "/directory";

Where directory is the directory for that MediaWiki installation relative to the DOCUMENT_ROOT.

This resolves issues where a user is occasionally prompted to log in when viewing a different installation, even though they logged in earlier and asked to have their password remembered.

$wgSessionName and $wgCookiePrefix provide alternate solutions.