The two brothers Julius and Johannes, in order to escape possible persecution, took the name of their mother Gertraud van Külchen (Kühlchen or Küelchen)[3]. The name Külchen came/occurs mainly in the area around Cologne. A hint that this spelling might be correct. How this name was pronounced phonetically at that time is not known. In 1564 a Külch is mentioned for the first time in the naturalization book, from 1576 on the name Köl resp. "des Kölen" is listed uniformly in the church books. So the surname Köl originated from the name Kühlchen, has therefore nothing to do with Kohl.
In 1650 an "h" was added for the first time, Khöl. From 1665 on, only the final version "Köhl" was used. Besides the noble title "von Köhl", which was preserved in 1684, several of the descendants also used the title "von Rogister" until the end of the 19th century.
Sources:
3: Sammlung Rätischer Geschlechter, Sprecher von Bernegg, Anton Hercules, 1847