Hotmail and Windows Live

The mail address in the Inbasket at Hotmail says -
but when I'm sending from Windows Live, it says -

I suppose I must have done something wrong from the beginning, when I was creating the account (?) On the other hand; if one is creating an account on Windows Live, it will automatically be the same on Hotmail, right ?

Can somebody tell me how to change it so it comes out the same on both places ? Very grateful for help ! :)