What kind of lawyer do I need to copyright a business name? What else do I need along with starting a small business? Refrences?

You would need an intellectual property attorney.

An intellectual property attorney.

This question is often asked by clients and the short answer is: you don't need to "copyright" a business name. Copyright only applied to someone literally copying your work. Typically, in the context you are referring to, you want to "Trademark" your name. A trademark prohibits the use of that name by anyone else whether they copies your name or logo or came up with an identical or confusingly similar one on their own without any prior knowledge or access to yours. In either case the type of attorney you'd be looking for would be an "Intellectual Property" lawyer. US Patent and Trademark Office charges $275-$325 per application, per class of goods and attorneys often charge as low as $500 to file your trademark application for you.

With respect to your question about "Legalizing" the name of a small business, you have several options that range in price and level of protection. You can file a Fictitious Business Name also referred to as DBA (Doing Business As) filing with your county recorder which will likely cost you about $100 including the publication costs and it will allow you to open a bank account under that business name and use it for your business but it does not offer you any liability protection for your personal assets in the event a claim is made against the business. You can also form a corporation or other business entity that offers you more protection. Approximate costs for CA are as follows:

* Do it yourself (~$150)
* Use an online document preparation service including corp kit (~$400)
* Use an attorney including corp kit (~$400)

You register a trademark, not copyright, a business name.
Additionally you should incorporate the business.
A trademark attorney, such as myself, can take care of both matter, expeditiously.