In 2293, the Springfield was assigned a Neutral Zone patrol mission. The ship was named on a Starship Mission Assignments chart on the USS Enterprise-A bridge. (Star Trek VI: The Undiscovered Country)
Springfield was said to be the most common town name in the United States of America, with 37 cities by that name (and many more with variations of that name, such as "Springfield Crossing" or "Springfield Plantation") in over thirty states. It was possible that one of these cities was the origin of this ship's name.