I don't know how big your name or logo is going to be on the shirt but if it's something small you might want to look into getting those iron-on transfer sheets that you make up in your computer.
The caveat is that you should cut out your lettering or logo so that it will look like you had it done at a shop and not something you made on the ironing board. If you ever notice, there are a lot of people wearing custom T-shirts that have the big 8½ x 11 rectangle smack dab in the middle. You don't want that. Also, if you want a design that's bigger than 8½ x 11 you'll be able to do it with multiple sheets of the transfer paper.