That's not your carrier name, it's the network name. It will change if you connect to a different carrier's network, although chances are you will stay with your carrier unless roaming.
You should try the theme "Morph". It lets you fully customize your home screen and one of the options is to hide EVERYTHING on the home screen. I check off a box and the "T-Mobile" goes away! "Morph" was on sale....it may still be.....