Here's what I found out about the name while researching my own grandparents.

Different documents show different places of birth for persons with the name Dyki. There are also multiple transcription (or understanding) errors made on the official documents. From my research, country of birth has been listed as Poland, Ukraine, Ruthenia, Austria, Hungary, Australia, and Scotland. The Dyki surname is native to an area that was part of the Austria-Hungarian empire called Ruthenia. This area is located on the borders of present day Poland and Ukraine. In the 1880's and early 1900's the area was represented most commonly as Ruthenia.

My grandfather, from Wayne, Michigan, went by William Dyki. But of course William doesn't really fit. I finally discovered his first name was Wasyl. My father's generation changed the surname to Dyke.