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.
Tim Berry is the chairman of Eugene, Ore.-Palo Alto Software, which produces business-planning software. He founded Bplans.com and wrote The Plan-As-You-Go Business Plan, published by Entrepreneur Press. Berry is also a co-founder of HavePresence.com, a leader in a local angel-investment group and a judge of international business-plan competitions.