I mean you just mistook Kara Atmaca for Barbaros CDS

I'm fine with calling land based Atmaca batteries as just Barbaros CDS. Kara Atmaca is more than a Harpoon with land attack capability. The difference is more similar to that of Harpoon and SLAM-ER. So I think it does warrant a new name that is different than Atmaca.
Operationally and doctrinally Barbaros and Kara Atmaca is of course very different. Organizationally as well, Barbaros will be delivered to the navy, while army is the customer for Kara Atmaca. Cruise missiles for army will be a force multiplier. Maybe army changes the name and navy only refers it as Barbaros for the land based variant.