They were previously known as the California Angels and the Anaheim Angels .
The team has gone through several name changes in their history , first changing their name to the California Angels on September 2 , 1965 with a month still left of the season , in recognition of their upcoming move to the newly constructed Anaheim Stadium in Anaheim at the start of the 1966 season . 31 of the team 's 50 seasons have been under the California Angels name .