Do you really want to change the name of the corporation, or just change the name that people know you by? You don't have to change the name of the corporation to change your marketing name and the name that others know you by. Acme Inc. can operate as Emerald Manufacturing with just a bit of paperwork called DBA for "doing business as" or fictitious business name. That alternative is common and it preserves your business history.
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.
Complex purchases aren’t so much about a product or service as they are about an outcome, a trajectory, a solution or a promise. To gain the right offer from a vendor, ask the right questions and look in the right places.