Also interestingly, I have read Sean Fagan's book 'The Rugby Rebellion' which came out in 2005 (I think). In chapter 4, there is a club-by-club summary of the formation of the foundation district Rugby Union clubs, and on page 57 it has quoted the 'Sydney Morning Herald' and 'The Referee' newspapers from March and May 1900, and this is an excerpt of what they had to say about the formation of Eastern Suburbs:
"...The name 'Eastern Suburbs' was once well-known in althletics and Cricket fields. About the most famous of the now defunct amateur athletics clubs was the old Eastern Suburbs club. Also in existence at that time was the old Eastern Suburbs Cricket Club. But since those days, until a month or so back, the name Eastern Suburbs had dropped out of the world of sport, and indeed, out of all others. It is now revived in football, but strictly it is a misnomer, for the area embraces a substantial portion of the city. That is however a mere detail..."
So even back then in 1900, it was acknowledged that the Eastern Suburbs name maybe wasn't quite right. And so it seems after all these years the 'Sydney Roosters' name is the correct one after all.
I know Sean is a regular poster on these forums. Perhaps Sean can elaborate and add to this further?
Only just stumbled upon your post...some random notes to add here...
It is correct that Easts covered much of the Sydney CBD, but looking at their founding meeting in 1900, they elected as Vice Presidents the Mayors of Sydney, Woollahra, Waverley, Randwick & the MLA for Paddington. I've got the exact list of club bondaries/suburbs in 1900 here somewhere, and I'll dig it up if time permits.
The club's spiritual home in 1900 was Paddington - the founding meeting was at the Paddington Town Hall, the club colours were those of the Paddington RU Club (the jersey design was copied the 1899 British team who had the same colours), and some of the early match reports in 1900 referred to the team as "Paddington".
In the years immediately before the 1908 start of RL there was a Sydney RU club that had been split off from Easts. But when the NSWRL formed they restored the original Easts district.
Under the NSWRL, around 1912-14 there was decided push to split away from Easts by a number of players/supporters to form a "Sydney" first grade RL club. One of the meetings was held at Dally Messenger's pub (which was directly opposite Museum Station in Elizabeth St - now the
http://www.queensclub.com.au/ ).
'The Referee' 29.8.1913 stated "Eastern Suburbs covers Watsons Bay, across to Long Bay, taking in Maroubra, Randwick, Coogee and Kensington, coming along Oxford and Liverpool Streets and along George St to Circular Quay
population of 183000."
The Rugby Rebellion is still available - re-issued & extended as
Pioneers of Rugby League.
http://www.RL1908.com/Pioneers/index.htm