Greeks have their own word for Balkans, Turks had their own… why use any of theirs, we are Slavs and we should have a name for the region fitting our language is it not true?

I agree, Slavs do use their names in their own language and will continue. Internationally we are called differently though (slav. Hrvatska -> lat. Croatia).

For the international usage, I would rather use it's original name Haemus, than it's 'new' Turkish name Balkan.