The Sydney Swans are called Swans because South Melbourne were called Swans and they were called Swans because so many Westrines played for them in the 20s and 30s.
From Wikipedia:
"It was during this period that the team became known as the Swans. The nickname, which was suggested by a Herald and Weekly Times artist in 1933, was inspired by the number of Western Australians in the team (the black swan being the state emblem of Western Australia), and was formally adopted by the club before the following season 1934.[19] The name stuck, in part due to the club's association with nearby Albert Park and Lake, also known for its swans (although there are no longer any non-native white swans and only black, indigenous swans in the lake)."
They've been doing it for centuries...