Xbox live create profile problem! HELP!?

So I had created 3 profiles on my old xbox before it broke and I got a new one under the warranty. I would like to make a new profile and get rid of my old one. but when I done so on the new console I was given no live membership. It generated a random name for me instead of letting me choose and now it's giving me the option to change my name. If I change it to my desired profile name will they allow me to have my rightful membership. BTW this was all done on the xbox live dashboard.