I think what you mean to say is not "Starlink is listing my position as ..." but, rather, "Online services I interact with are interpreting my location as ...'
Some services, often streaming media services or shopping web sites, will try to interpret your physical location based on the IP you're connecting to the Internet with. In Starlink's situation, the ground station or datacenter where the sats you connect to actually interface with and connect to the Internet from may be dozens or hundreds of miles from your physical location. There is zero you can do about this. It is just the nature of the networking involved. This has been true with any ISP for a long time. I live in central MN but when I was using AT&T for Internet everything thought I was in Chicago.
Any service that enforces rules based on location, primarily streaming media services, typically has a method to verify your location in another way. For instance, with YouTube TV they will have you go to a web site on your phone and give your browser temporary phone location permission to verify where you're actually at. Contact those companies and ask for how to deal with the situation. For online shopping sites that try to find "closest store" I don't think there is any way to fix that.