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.
Anke Katrin Eissmann is a German illustrator, mainly known for her beautiful Tolkien-related drawings. She has a lot of nice pictures of the characters, especially of Faramir.
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]