The early years were hard. At times the settlement was on the verge of abandonment by isolation. One problem was the determination of the beavers to interfere with irrigation. Beaver Dams but the name eventually became Littlefield for one of the first families. Best guess is that it came from the early Spanish, perhaps Father Escalante, with their love for names of the saints and the Virgin Mary.
Old maps show the Spanish spelling of virgen.
Littlefield people are understandably less enthusiastic about being Arizona residents than most. They send their children to school in Nevada and read the Utah papers. It is the same driving distance from Pheonix as Los Angeles. This article was given to me by Dessie Reber Staheli out of her many scrapbooks from through the years.