I'd love for them to go back to the "Easts" Roosters emblem (or silhouette) currently emblazoned on most of the other merchandise they sell. Solid blue Rooster within the white or red of the Home jersey V, and whatever other colour works on the alt/away jerseys.
Yes it's very Souths, and to a lesser extent Panthers and Phins, but I think it would only serve to fuel the Rabbitohs rivalry even more when you see two traditional Sydney teams playing with the more traditional emblems.
Hell you could even trial run it as an alt-heritage jersey (perhaps a versus Rabbitohs only jersey) that they can gauge interest on for a more permanent change?
In terms of name: I think going back to adding the word "Suburbs" in the name is regressive in a sense it makes the team appear very small. Sure, you may bring some short lived joy to older die-hards that remember them before the Sydney City days, but a proper area qualifier akin to "Eastern Sydney" would be much better in that it bridges new fans with the old and gives the team a more accurate locale identifier.
What I think we should DEFINITELY steer clear of is the Wests Tigers solution. Unless you had some basic understanding of the NRL and it's teams and history, what "West" are you referring to? If I was new to the country, state or new fan generally, I would immediately assume "Wests Tigers" were on the West Coast. South Dragons (NBL) have the same problem, Western Force (RU, I think) and Western United FC (A-League)... it's all meaningless and can even drive a disconnect if you're not actively wanting to look into their location or a fan of the league already.