how do you change your Apple ID "name" (display name)?

I recently got married and legally changed my name. I am now trying to change my apple ID name but it seems to be impossible?

Secondly, I also use a me.com email address as my main email ID and this is also in my maiden name with no option for me to change it?? When i go to mail preferences > accounts> and then try to change display name it is also grey'd out so that you cannot edit it. Very frustrating - Please help!?

(In every other web email account, i have been able to change the display name of my emails)