I feel the whole Dragons vs Saints thing has become a little generational and a result of the JV.
St.George Illawarra really pushed the Dragons branding from '99 onwards as a unified banner for the new team and I reckon that anyone who was born 1995 onwards will know them as The Dragons and anyone before that is Saints.
As a kid of the 80's and 90's I grew up knowing them simply as St.George or Saints for short. We chanted Saints or St.George on the hill, all the merch had just St.George or Saints on it, even our emblem (and still to this day) is the only one that doesn't have the name of the mascot plastered across it, ours simply said St.George and post JV St.George Illawarra. And personally, I hope it stays that way.
I do remember Dragons being around as a secondary name and the St.George bank dragon was always at the grounds, but I don't remember a mascot being as prominent a thing as it has become in the post Super League and professional era of Rugby League where branding and franchise have become more important, or at least more recognised, than the teams location.
I really prided myself on calling the team St.George or later on St.George Illawarra.
I grew up in Bondi and supported Saints and grew up in a St.George family so for me it was a real pride thing that I really related too. More so than a Dragon.