Is "the Healer" (al-Tabib) one of Allah's Names?

Allah Almighty is described as "the Healer" (At-Tabib) in several Prophetic hadiths, including those of Abu Rimthah and Aisha. However, it is not permissible to absolutely name Allah Almighty as "At-Tabib" without qualification, because the names of Allah are divinely ordained (tawqifiyyah) and can only be established through textual evidence.