Is it advisable to change your name before hysterectomy, due to damn insurance companies possibly denying hysto coverage for it? or does it even matter? I've heard that you should wait until post-hysto to change the F to M, but what about your name?

the first sentence should read *after hysto* not before

In the top right corner of your post, you can click the "modify" button and edit your post if you want. 
And sorry, I don't know the answer 

it doesnt matter about your name, people change their names all the time. its changing you gender marker, that can cause problems with your insurance coverage.