Two of my great-great grandparents have the name Duddy - Mary Duddy Walsh and Sabina Duddy Mullen from Co. Mayo.
Mary (spouse unknown) married a Walsh, had son James 1840-1850. Sabina married James Mullen, had daughter Anna/Hannah/Hannorah/Honora also 1840-1850. James Walsh and Hannah Mullen were married in Ireland about 1867 and emigrated to Warrington England where they stayed for 5-8 years, had 3 children (Sabina, Bridget, Mary) and then emigrated to the Youngstown Ohio area in the 1870's. Duddy is not a very common surname. Do you know whether your James Duddy had any siblings?