Frisian, North German, and Dutch: patronymic from a pet form of the Frisian personal name Onno.

according to the " dutch family names bank" :

Uneken, Unk: Patr. Dim. van de Friese VN Une, Unne, Oene, Onne, Onno. 1397 Oncke Snelgers; 1527 Ineke Oneken

Onken (NN). [WFZ]

 WFZ is an abbreviation the Dutch Family Names Bank uses to refer to the Woordenboek van de familienamen in 

Zeeland (Dictionary of family names in Zeeland) by Frans Debrabandere .

The lemma shown by the Dutch Family Names Bank is from that book.

What it says is that Unk and Uneken are patronymic diminutives of the Frisian given name Une, Unne, Oene, Onne and Onno.

99 Onkens signed in at Ellis Island, Three in 1894 aboard the "Noordland" one of which was my grand father, his older sister and brother. A year later his father and and mother, Heinrich and Gretize onken (Aden) shipped out aboard the "Belgenland" along with two younger daughters,Else and anna.