here's what you need to do.
Create a profile on the Xbox right now. You probably were made to create one anyway. When that's done, you want to pick the option that says "Join Xbox Live". That will ask you for you Live ID/password. Use the same one you used on your phone. It will attempt to use the GamerTag you set on the profile you have now on the Xbox. If that one is taken, it will make you pick a new one. The new one will be the one that your phone and Xbox will use. You shouldn't need to do anything on the phone, it should auto-detect the change and use your new gamertag.
More info here:
New Xbox 360 Console | Xbox Console Setup | Join Xbox LIVE - Xbox.com
p.s. You don't have to make the Xbox Live profile be a Gold one (which requires a yearly subscription). A silver one works fine.