The name Werneke exists both in the Netherlands and in Germany. It has various alternate spellings: Werneke, Wernicke, Wernecke, Wernigke, Warneck, Wernink, Wernekinck, Weernink, Wernke, Wennink, Warnink, Werning, Wernik.
Pronounciation: (/ˈvɛərnɨkə/ or /ˈvɛərnɨki/; German: [ˈvɛʁnɪkə])
In German -icke is a diminutive, so Wernicke means "little Werner". The meaning of Werner you can read here: http://www.behindthename.com/name/werner And in German language here (a lot of info which is too techical and extensive for me to translate in English): http://www.rambow.de/download/Genealogie-Wernicke.pdf
In the North-East of the Netherlands it is an addressname (farmname). Originally the Saxo suffix -ink was a patronym ("belonging to the family of..."). Round the Middle Ages however it lost its patronymic function, and it was used in combination with addresses (farms etc). It might even be the following Wern-farm in Hoogeveen, Drenthe, the Netherlands (photo): http://www.mijnalbum.nl/Album-BLMQ6ZQ6-Foto's-in-Hoogeveen-Foto's-van-Huizen-en-straten.html. The name Wern is related to the German name Werner.