The name Anke is derived from the Hebrew name Hannah (also Channah) meaning "Grace", "Graceful". It is a German name which is also widely used in the Dutch, Swedish, and now more recently, Afrikaans (born from Dutch) languages.
Apart from Anna, it can also be short for Anne or any other name starting with An- since it´s basically that combined with the Dutch diminutive suffix -ke. My aunt´s name is Anke and in her case it´s short for Annigje which is a diminutive of Anne itself. [noted -ed]