The city of Irving was founded in 1903 by J.O. "Otto" Brown and Otis Brown.  It is believed that literary author Washington Irving was a favorite of Netta Barcus Brown, and consequently the name of the townsite, Irving, was chosen.  See the photos below that show how the city of Irving has changed through the years.
(Click the photos to enlarge them.)
 

Main Street in Irving - 1912