William Frederick Cody(1919-1989) and Ladora were the children of Charles Deloss Cody. This Charles was the son of George Washington Cody who was born 1875 in Ohio and died 1963 in Tulsa, OK. George's father was John Cody, Jr. who was born in Ireland 1849 and died in Ohio in 1926.
John Sr. was born in Kilkenny (Ireland) and died in Ohio in 1888. Naturally, since this family originated in Ireland and immigrated to America in the 1800's, they are not in any manner related to "Buffalo Bill" by the Cody surname. Nevertheless, it's quite likely that "this" William Frederick Cody was simply bestowed the full given name, if proven to be so, as a kind honorable tribute to the famed frontiersman- not an uncommon gesture by many Americans, whether of Irish origins or not. :)