There's currently the tag klingon and the tag klingon-language. As Klingon is probably the most famous fictional language around, it having a separate tag from Klingons in general is justified.
However, some questions currently in klingon are solely about the language, and so should be retagged accordingly.
(For those wondering about the question title: see Who owns Klingon? Lawsuit draws battle over invented languages into court)