Are you aware that when you send e-mail with hotmail that your full name that you signed up with is showing to all? If you don't care then leave it, otherwise do the following.
Go into your hotmail.
On the left hand side it says options, click it on.
A new screen comes up, click Profile on.
Where it asks for your first and last name use your screenname or something else. For instance I use mine as Angel Bear, breaking apart my screenname so that shows when I e-mail others.
Its safer not to give your real full name to those you don't know.