After you make an account and upgrade it to Xbox Live Gold it will automatically give you a random gamertag then after that you can go on your Xbox console or on the computer and change it one time for free. After that it cost 800 Microsoft points (10 Dollars
USD). Hope this helped if you have any other questions message me!
I have never got a random Gamertag from transferring from Silver account to Gold & kept the NanoTechSoldier Gamertag I originally signed up with on the Silver account etc..
There is an easier way to get a Free Xbox Live Account too..
When you turn your new Xbox 360 console on.. Click on Create Profile & choose a Gamertag name.. Once your profile signs in, Press the Guide Button in the center of the controller & then click
Join Xbox LIVE, to enter your chosen e-mail address & password for the account & sign up to Xbox Live
It keeps the name you have chosen on your Profile & Won't randomise any name.. (As long as no-one else has the name you have chosen on your profile etc)