Cook County-- Named for Daniel P. Cook, a pioneer lawyer, first Attorney General of the State of Illinois and Representative in Congress from 1819 until his death in 1827.
DuPage County -- The county took its name from the DuPage River, which was, in turn, named after a French fur trapper, DuPahze.
Will County -- Named for Dr. Conrad Will, a businessman involved in salt production in southern Illinois, and also a politician. Will was a member of the first Illinois Constitutional Convention and a member of the Illinois Legislature until his death in 1835.
Kane County -- Named for Elias Kent Kane, an attorney who helped draft the Illinois constitution and was the first Secretary of State. Kane was later elected to Congress and represented Illinois in the U.S. Senate until his death in 1835.
Further reading at Origin of County Names Illinois Blue Book, 2009-2010.