Massachusetts instructions say to add the rental car to your account, but I've used my own EZPass a bunch of times there without problems and without getting double billed. I live in CA, but have an MA EZPass that's registered to my CA license plate and address. It's only ever been used in rental cars.

ETA: my solution to leaving it in the rental car is to tie a thin, bright colored string to it that hangs below the mirror. I put enough string on it that I can attach it t a carabiner on my backpack in the passenger seat. I only just started doing the string after I left it in the car in December, after years of not forgetting it. Fortunately I had a ton of time before my flight and had time to take the shuttle back to Hertz and wait around while they found my car and the transponder (I wrote them a very nice review for that)