You can’t copyright the name of your company.
You might be able to trademark the name or a portion of the name, if that makes sense.
So, what is the difference?
Copyright protects how you say something, and it isn’t available for names or short phrases.
Trademarks (and service marks) identify your company as the source of particular goods (or services).
You probably want to get some professional help if you are considering scaling up the value of your intellectual property (IP).