ANSWER
The team known today as the San Francisco Giants began in 1883 as the New York Gothams. The new team was formed to replace the Troy Trojans, who were voted out of the National League. In 1885 they became the Giants, and in 1957 they moved to San Francisco. (A move coordinated with a similar move to Los Angeles by the Brooklyn Dodgers.)
The team known today as the Anaheim Angels began as an expansion team in 1961, when they were known as the Los Angeles Angels. In 1965 the franchise, owned by Gene Autry, began building their own stadium in Anaheim, and changed their name to the California Angels. (They moved into the new stadium in 1966, after playing the previous four seasons in Dodger stadium.) In 1997, they became the more specifically named Anaheim Angels.
WHO GOT IT RIGHT: JP Weigt, Bob Milligan, Debbie Boudreau, and Steve Jones.