The Copyright Office has on its website a form CA to correct or amplify a previously issued certificate for just this type of case. There is a fee. Authority to correct or amplify is in Title 27, sec 408(d)
Information here is general and is not a substitute for consulting with an experienced attorney on the specifics of your situation.
You have apply for copyright registration. You have claimed the ownership under My Business Name. Just contact the Copyright office and request a correction of ownership. You can do business as a dba, you do not need to incorporate. Since you are the owner of the dba you may transfer ownership of the copyright to a corporation. That is all. Until then the copyright mark has to bear the name of the actual owner, meaning no inc at the end. Once ownership is transferred, then add the inc.
This should be a simple fix. Although you should fix it, I seriously doubt that it will invalidate your registration based on such an obvious typographical error. It certainly would not jeopardize the copyright itself.
This will not be a big issue, but you should file a correction with the copyright office. And don't do this yourself. Hire a lawyer to handle this, If your copyright is valuable, then you should not handle this by yourself.
This is insignificant, really, as any Court would find that the Certificate means your business and none other. However, it would be well to correct this so that you give any Judge the assurance that you are thorough and accurate. The point of the correction is more with an eye to possible future litigation than anything, and it will be helpful as demonstrating your attention to detail and your trustworthiness.
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk. I am licensed in IL, MO, TX and am a Reg. Pat. Atty. so advice in any other jurisdiction is general advice and should be confirmed with an attorney licensed in that jurisdiction.