> It's not 'dansk tunga', but Norroen(a).

You're both right - "dönsk tunga" or "Norroena".

The term "dönsk tunga" is also used to mean
"the territory where Norse is spoken" as in this text:

"En fyrir því at Fróði var allra konunga ríkastr
á norðrlöndum, þá var honum kendr friðrinn um
alla danska tungu..."

My translation: "And because Fróði was the most
powerful of all kings in the northern lands the
peace was attributed to him in all the Norse
speaking world..."

Kveðja,
Haukur