Douds Iowa was named for English descended Douds (Eliab, David Jr. and Stanford amoung them) They were all sons of David Doud Sr and his wife Fear Beaumont.

Mamie Geneva Doud was from another line of the family. According to the O.L. Doud book:

Henry Doude and Elizabeth Dadson (Of Kent)> John Doud and Mary Bartlett > David Doud and Mary Cornwall > Richard Doud and Phebe Foster > Benjamin Doud and Mary Savage > Eli Doud and Maria Riggs > Royal H. Doud and Mary A. Sheldon > John S. Doud and Elivera Carson > Mamie Geneva Doud.

To connect with Irish Douds you would have to go back to 1609 or before I am afraid...