The club is officially known as "Sydney University Football Club" because it was the first club of any football code in NSW. The club also played Australian rules football in its early history, making it the first NSW club in that code as well.
The club is often referred to as the "Students". Its nicknames have also included "Quizkids" and "Varsity". It is also referred to as "The Birthplace of Australian Rugby" or simply "The Birthplace".
Over one hundred Sydney University players have been selected to play for Australia. The first Australian representative was Hyram Marks in 1899. The club's most famous Wallaby would probably be Nick Farr-Jones, who had a long representative career (including World Cup success).