the law ---------as i understand it

you canNOT copyright a name

you can trademark a name that has been used in interstate commerce
go to the PTO website and read all about it

start now by googling for a name and make sure nobody is using it
if so start using it asap with a TM mark
as soon as you can sell something interstate
spend the money and REGISTER the name then use the circle R symbol

you will need to register the name with your local/state govt agencies
and do other things they require to run a biz - which may not be legal in a home (or not) depending where you are