Manual:$wgDisableAnonTalk

Recent changes, new pages, watchlist and history: $wgDisableAnonTalk
Disable talk pages for anonymous users (not logged in).
Introduced in version:	Before 1.1.0
Removed in version:	Still in use
Allowed values:	(boolean)
Default value:	false
Other settings: Alphabetical | By function

Details

Disable links to talk pages of anonymous users (IPs) in listings on special pages like page history, recent changes, etc.

This does not disable the talk page itself, nor does it remove the "mytalk" link anonymous visitors see on top of every page. For that, use the PersonalUrls hook to remove the link to the talk page of anonymous users:

$wgHooks['PersonalUrls'][] = 'lfRemoveAnonUserpageLink';
function lfRemoveAnonUserpageLink( &$personal_urls, $title ) {
	unset( $personal_urls['anontalk'] );
	return true;
}