Mich. Const. art. III, §7 provides:
The common law and the statute laws now in force, not repugnant to this constitution, shall remain in force until they expire by their own limitations, or are changed, amended or repealed.

Piotrowski v. Piotrowski, 247 NW 2d 354 - Mich: Court of Appeals 1976 provides:
Under the common law a person may adopt any 216*216 name he or she wishes, without resort to any court and without any legal proceedings, provided it is not done for fraudulent purposes. See Kruzel v Podell, 67 Wis 2d 138, 151; 226 NW2d 458, 464 (1975), Petition of Hauptly, ___ Ind App ___; 312 NE2d 857, 859 (1974), Egner v Egner, 133 NJ Super 403, 406; 337 A2d 46, 48 (1975), Application of Lawrence, 133 NJ Super 408, 411; 337 A2d 49, 51 (1975), In re Marriage of Banks, 42 Cal App 3d 631, 637; 117 Cal Rptr 37, 41 (1974), Application of Halligan, 46 App Div 2d 170, 171; 361 NYS2d 458, 459 (1974). There is no requirement that any person go through the courts to establish a legal change of name. Thus, even if a woman changes her name upon marriage, there is nothing which forbids her from changing her name back to her maiden name, or any other name, provided it is not done with fraudulent intent.

In Michigan, as in most states, a statute authorizes procedures by which a court can, upon petition, change the name of any person. MCLA 711.1; MSA 27.3178(561). Such change of name statutes do not abrogate or supersede the common law. To the contrary, they affirm the common law right and afford an additional method by which a name change may be effected as a matter of public record. Kruzel v Podell, supra, Petition of Hauptly, supra, Egner v Egner, supra, Application of Lawrence, supra, In re Marriage of Banks, supra, Application of Halligan, supra.

IN RE WARSHEFSKI, Mich: Court of Appeals 2020 states:
An individual may adopt any name he or she wishes, without resort to any court or legal proceeding, provided it is not done for fraudulent purposes, under the common law. Id. Under the common law, and in the absence of fraud, a minor may also adopt any name he or she wishes provided they are of sufficient age and maturity to make an intelligent choice. Rappleye, 183 Mich App at 398.

AG Opinion No. 7142 provides:
The Michigan Secretary of State may, but is not required to, accept an affidavit alone as sufficient legal proof to effectuate a common law name change on a person's driver license.

A Michigan Live article from 2013 suggests DMV policy at the time allowed common law name changes if you showed 6 months consistent usage:
But the SOS denied the common-law name change request, in part, because Jesse had not been living with the name for six months.