Yes, Wayne County courts are not "user friendly!"
We joked about moving a couple miles north into Oakland County because I could figure out exactly what to do
there!
Anyway, you need to contact the Third Judicial Circuit Court - Family Division - Juvenile. 313/833-1961. They are located at the Lincoln Hall of Justice 1025 East Forest Detroit 48207. It has been about a year and half since we did our kids' name changes and delayed registration of foreign birth, but I am assuming it hasn't moved since then.
Good luck! PM me if you have any questions about it.