If you want to do the designs yourself you can start with the program GIMP at
GIMP - The GNU Image Manipulation Program. It is a free image editing program that is relatively powerful.
I say, if you aren't that good... leave it up to someone who is. It may be possible to find another kid at your school who is good at design and will do this thing with you. Instead of trying to come up with designs that might be sub-par, you could spend your time doing things you are better at. You may be better at the business side, or the printing side. Save up to get some equipment, or find someone who will do it for cheap. Come up with another way to make shirts that don't require a substantial financial commitment.
As far as a name goes, you can sit around and think of names forever. If you cant find something you are 100% in love with, just pick something. There are a lot of ridiculous names out there. Your clothes are what makes it cool.