Changing a local listing (address visible) to a service area business (address hidden) is pretty straightforward although not as intuitive as the previous iteration of the Google My Business dashboard.
 

Change Local Listing to SAB Listing

You do need access to the Google My Business Listing, if you have not claimed ownership, then you must do this first to be able to manage your business listing.
 

1. Log into GMB Dashboard

Log into your GMB Dashboard – https://business.google.com/locations
 

2. Info Section >> Select Address

Select the info section, then click on the pencil icon next to the address.

 

 

3. Remove Address Details

The previous dashboard had a tick box, but in this new version you need scroll down ever so slightly to revel the >> Clear Address.
 

 

Select >> Apply
 

4. Select Service Area of Business

If you do not select a service area, it will default to the entire country.

I prefer to select the suburb, town and county (state) – naturally you can also select multiples of these.
 

 
Note: Selecting the entire country as your service area will not result in your listing being displayed for every search query around the country.
 

5. Check the Listing

The changes will remain in pending for a little while. Refresh the page and when they are applied, do a quick check on your listing and how it is displayed.

In the Info section >> Select >> View on Maps
 

 

See: Will changing my listing from a local listing to SAB listing affect my rankings?