Glad you are thinking of going down the indie route- after 7 months you will be more than prepared, and sounds like you are on the cusp of taking the leap anyway
I've never told my indie clients that I am with an agency, or vice versa- no need to! And apart from one guy who asked if I was blah blah on an agency site as well, no one has ever mentioned it. Even easier if you don't show your face. Also, (although I am sure this isn't a hard and fast rule), I find that a client tends to favour either indies or agency girls, and is unlikely to peruse the world of both, so it's unlikely anyone will find you if you keep separate personas for both.
Having said that, as Alex said, does your agency stipulate that you can't also work independently?! If not, you've got the option to be the same girl in both spheres- it's a free world and you are simply being business savvy! And this might be easier, as I do find it tricky at times having to remember whether I am me, agency me, and indie me