Teams named after animals are popular because animals generally have characteristics that are desired qualities of a softball team. For example, foxes are smart, tigers are aggressive, lions are brave and dolphins are smooth or elegant. You can name your softball team after an animal with a characteristic you want your team to share or use to intimidate other teams.
Schools or individual softball teams often find a characteristic of their town or city they can use to associate with the program. For example, a team out of New Orleans may go with "the Jazz" or something that represents the history or culture of that city. A team from New Mexico may go with "the Armadillos" or a team from Michigan may use "the Great Lakes."
Some nicknames are inspired by characters of the past. For example, the Spartans, Warriors and Gladiators are common names for softball teams because they represent relentless fighters or competitors. Groups of people are also fun and common, such as the Vikings or the Cowboys.