The form you need is an Certificate of Amendment to the Articles of Incorporation. It is form 515, which you can find, here: http://www.dleg.state.mi.us/dms/results.asp?docowner=BCSC&doccat=Corporations&Search=Search
For item 3 you would state the new name of the Corporation.
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Well, I think before you do anything you may want to discuss the issue over with a business or trademark lawyer to make sure you would be required to change your corp name. It is entirely possible for two businesses to operate under the same name (not usually registered in the same state without a DBA) particularly if they are involved in unrelated goods or services (e.g., Delta Airlines vs Delta faucets).
If you do require to change your name, you can file an amendment with the secretary of state and for a nominal fee you can make that change without the need to go through the entire reformation process. This does not come up that often, but I also believe you can submit a corp name change form to the IRS so that is reflected there as well.
Again, you should consult a lawyer before you make any changes just to be certain you are going about this the right way. Most of us here, including myself, offer a free phone consult.
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