GitHub Desktop is a graphical user interface (GUI) for working with Git and GitHub, it is not available as a package on Homebrew package manager, which is a package manager for MacOS.
Homebrew is a command-line tool that is used to install and manage software on MacOS. It is not typically used to install GUI applications like GitHub Desktop. Instead, you can download and install GitHub Desktop for MacOS directly from the GitHub website, as I described in my previous answer.
It’s worth mentioning that there are other package managers for MacOS like MacPorts and Fink, but GitHub Desktop is not available as a package on those package managers as well.