It is good that you do see there is a visible Church. Some on here don't.
Now how would Paul know your assembly to address? How many "assemblies" would he be writing to in your neighborhood? In your zip code? In your city? In your state?
I dont identify my location. It really doesnt matter does it. Wherever two or three are gathered in my name becomes and assembly where Christ is present. All believers are after all called out in His name.
Just prior to Thanksgiving, my mega-church was involved in a food drive. They were joined by a number of other local churches. In the written materials and on the news stories, all the churches were referenced as The Church of Cincinnati. They all agreed to not be named otherwise.
I suppose a letter could be delivered to one church leader, read and then passed to the next.