Ainsworth Iowa was named after Danforth Hurlburt Ainsworth. He was an engineer on the Rock Island Railroad when it extended its tracks from the Mississippi to the Great Southwest in about 1858. Danforth and his wife Sarah donated 40 acres of their land for public use and was dedicated October 11th 1858. I have been there twice (long drive from Jersey), my brother went to Ainsworth Nebraska for me once.
Ainsworth Nebraska was named after Capt James Edward Ainsworth (civil engineer) of the Fremont, Elkhorn and Missouri Railroad. There is still 15 miles of track left and there is a quaint dinner train that rides upon those tracks. I road on that dinnertrain last November and they made a small announcement that a descendant of James Edward Ainsworth was on the train. It was too complicated to say "x" cousin so many times removed".
Ainsworth British Columbia was named after George J. Ainsworth who was a promoter of the Kootenay Railway and Navigation Company. His father J.C. Ainsworth ran the Oregon Steam and Navigation Company. One his engines is still in existence. OR&N 197
The south side of Chicago was formally known as Ainsworth Station. There is an Ainsworth Wisconsin and Indiana that I am still researching.
James Edward and Danforth Hurlburt are both descended from Edward.
I do not know if you are an Ainsworth or not. But many of Edwards descendents worked on railroads and trolley systems. I just recently added myself to that list this past February when I took a job working in the PATH tunnels that are being restored under the Hudson River to Ground Zero.