I am making a case for my tools and I am looking for some thin safe sticky vinyl that I can cover it to make it look nice..

Does anyone know what it would be called and where on the internet to get some

Automotive vinyl should work. They sell adhesion promoter sprays in case you need more adhesion too. Check ebay/Amazon for various colors.

I use vinyl wrap to decorate car interior trims (real car) and such. Mine are simulated carbonfiber look (3M).
Don't forget the heatgun.