Sorry, but don't quite understand what the problem is. If you want a new hotmail account, you understand that you don't have to actually put your christian name and surname as your 'name'. For example you could put 'Computer' and then 'User'. Obviously this isn't part of your email address, which you have to choose further down the form. And if your chosen email address ('soandso' @ hotmail.com) is already in use you will be offered suggested alternatives.
Also, on your other thread there was a suggestion that you couldn't have more than one name on one address. Of course this is correct, but I assume you understand this is referring to your email address, not your postal address!