So if you have installed everything correctly, the file that actually starts the game itself is the fallout 4 script extender executable, located in your Fallout 4 GOTY directory. The file name is f4se_loader.exe.

However, the file that is run when you click the "Play" button in GOG Galaxy is the launcher for Fallout London, which is located in the Fallout London directory, and is named installer.exe.

Hope that helps. As to where those directories are located, I'm afraid that depends on where you chose to install them to on your system.