https://satellitemap.space have updated their real time display of the positions of the Starlink satellites to highlight the active coverage areas, like so:


Go to https://satellitemap.space to see real time now.

I guess that each ground gateway site can serve several satellites provided they are visible to the gateway site. Each of those satellites will have its own coverage underneath and if you can see the satellite and the gateway can also see it simultaneously you will be able connect to the internet.