Congrats! Your little cutting will grow into a beautiful new bush with time. Most of those minis sold in grocery store don't come with names. Some of them have names but the growers don't supply them to the sellers. That way they can substitute any pink rose they have on hand to fill their orders from the stores. You might be able to go online to the growers site and see if they have named roses listed. But, from there all you can do is try and match your rose to one of the names listed. It isn't easy. As Mike said, there are thousands of roses and the majority if them are PINK! Unless yours has some kind of distinctive trait it will be very difficult.
