If you want to actually change the name of the corporation, then you'd have to check with an attorney about the rules in your state. Details are different for different states.
As to how you do it, your first step is to contact a local attorney with small business experience. It shouldn't be expensive -- this is bread and butter for a small business attorney.
Rosalind Resnick is a New York-based freelance writer, entrepreneur, investor and author of The Vest Pocket Consultant's Secrets of Small Business Success.