My website is just showing up if I search it in the top bar of google writing the address “www.michaelmoraine.com”, but not if I search “Michael Moraine” or even “www.michaelmoraine.com” in the search bar at the center (the usual search method).
How long do you take your store live?
Did you verify it on Google search console?
https://search.google.com/search-console/welcome
Also it will take a time for google index your store to appear on search