In Latin, it would be Barbara/Barbarus, but the idea of Latin doesn't have a strong presence on Harqual, so I'm not sure that is the way to go. In Norwegian/Swedish, it would be Barbar. In Finnish, it would be Barbaari. Harqual is heavily influenced by both Norwegian and Finnish myth, in some ways, but there are also Greek deities too. If I had to choose, I'd probably go with either Barbarus or Barbar.
In Greek, it would be Várvaros.
The Barbarian language is tied to the North Gods and was born when Cronn first appeared out of Kulan's arctic and the first Northerners were formed by his tears after meeting the World Goddess, Mirella. In a sense, Northerners could be considered the Children of Tears (or Barn av Tårene in Norwegian).
Most of the peoples of the Northlands (including Harqualian Centaurs) speak either Barbarian or a regional dialect of it. For example, the Northerners of the Twilight Valley near the Greystone Mountains speak a version of Barbarian called Waracou. There is also Ismand, which is spoken all across the Northlands but not spoken anywhere else. It is a lot more uncommon and hard to learn (two skill points).
FYI, Common has its roots in Barbarian, but it is now its own language with its own alphabet. It is also called Harqualian. Barbarian, Ismand, and Waracou do not have alphabets or are written down in any form. When Northerners write, they use Common or another regional language such as Denilian, Kieli, or Sprache.
I'll upload my latest version of Harqual's language document in a moment...