No-one's completely original. I think to not carry a bag one truly likes because other people carry one like or similar to it, seems like a waste.
I always have some sentimental attachment or memory attached to my bag, whether it was an impulse buy with an awesome SA (MBMJ), for Grad but with a-less-than-enthusiastic SA (Chanel), something I excited scored at Winners or on Bluefly (RM), or something I got as a final gift from Gramps on vacation (my Bal.) I think a personal story attached to a bag - and I don't like to get attached to things, but none-the-less - adds a certain something that can make a bag one's own, even if it was an It bag at some point in time. My bags are special to me, even if they're just Bag #12663437 for the public.
Personally, I've gotten used to the fact, at some point in time, someone will be seen with my bag in the city. It happens. Providing we're not wearing near-identical outfits or look like the Bobsie Twins (or was it Bobsy?) I'm okay with it.
Though LV and Coach are both - for whatever reason - very popular here (I couldn't walk 5 minutes this afternoon to get a Subway sandwich and a Vanilla Coke without seeing three Mono Coach's), I still find LV classic. Worn with a more unique outfit, and I don't think anyone will notice that they saw two or three girls before you carrying a Speedy, as well.