Within your Google Business Profile and many listing Aggregators you can choose to make your physical business address visible or keep it hidden and only provide a list of areas (cities and counties) that your business serves.
Most businesses are very liberal when they select their services areas and in our experience they stretch themselves too thin. Context is key here so when you define your services areas consider the context of the service area for your paid advertising vs the context for your Local SEO.
This is the area you are willing to pay placement for and must be strategic. For example for home services these could be high dollar neighborhoods that are worth the extra drive time.
The Local SEO Service area is the geography you can claim where you have relational capital. Citizens are familiar with your business, people see your signs or your trucks, and you can back this up with reviews on your Google Business Profile from people in this service area. The point is to be practical and reasonable so you win the 'near me' searches on the Google map. Stretching your service area in hope for placement with the 'near me' searches from 40 miles away is not only a fruitless effort but will 'dilute' the strength of what is reasonable for your service area.
Only after you get strong placement in your smaller service area, should you consider stretching it.
TLDR: It is better to define a service area that is too small and rank 1st and 2nd all the time, then to have a service area too big and not rank at all.
There are a few things to be aware of on whether or not to have your address shown:
Local SEO