The problem is that LanguageKa.php has the Project namespace hard-coded. Thus,
Wiktionary's namespace inherited the name. How to set the Project name without
putting it in LanguageKa.php? (The default 'Wikipedia' and 'Wiktionary' will not
do)

Please update SITENAME ($wgMetaNamespace) for the following sites for KA language:

Wikipedia: ვიკიპედია
Wiktionary: ვიქსიკონი

I'll submit new LanguageKa.php file after (can only be after) this is done.

Any news on this? Come on, guys... Is it that hard to change?

The LanguageKa.php file changes are submitted on bug #3905 after this issue is
completed.

robchur wrote:

You ask for the sitename ($wgSitename) to be changed, but then state that you
want the meta-namespace ($wgMetaNamespace) to be changed. Which is it, please?

As according to most LanguageXX.php files:

if ($wgMetaNamespace === FALSE)
$wgMetaNamespace = str_replace( ' ', '_', $wgSitename );

, I would say it's $wgSitename which in this case will happen to be the same as
$wgMetaNamespace.
Please change $wgSitename (affecting the {{SITENAME}} variable).

Synced live site.

Fixed sitename too.