If you are working the name into a design as others have said, it would be fine.
There are several ways to use branding in your products as a start up.
As a start up company, you defintely don't want to just print your name and logo on shirts unless you are selling a specific product line. For example under shirts or underwear, you may want to use a small tag or print of your logo somewhere on the product.
Branding should be a part of every product. It dosen't necessarily have to be your full name printed on a shirt for someone to notice. It could be a design that you add your monogram to somewhere on the same spot of each product.
It's ok to get inspiration from well known brands, but think of a unique way of branding.
Did I totally get off topic? Sorry
