I need to change the mail address on the account in the Asset Store, but I only see how to change name, address, password.
Just made a new account after reading this, clicked the confirm my account link and was taken to this page - Unity ID
You can sign in, and edit your account from there 
It appears to be impossible, as apparently your e-mail address is your Asset Store login. Check this out:
http://forum.unity3d.com/threads/102628-How-can-I-change-the-email-in-the-Asset-Store-profile
So, in short, what you have to do is create a new account with your new e-mail address. The one thing I’m gonna have to find out manually is if your download history is preserved across accounts… here’s hoping!
As of 2016, you CAN do this! This question has been answered here:
https://support.unity3d.com/hc/en-us/articles/210176013-How-do-I-change-the-email-address-attached-to-my-Asset-Store-Account-