True, I think you can't change your name as well... there a few things that are fixed, but most you can change and it's advisable to give your profile a good overhaul make sure everything is correct and best aligned to you current situation as possible.
Indeed, that's precisely why I said - so long as you remain eligible and don't fall below the CRS cut off
We still haven't addressed the issue of claiming WE whilst not qualified to do so... @uppperkut I suggest you also ask this in Stanlee's Post ITA thread.