The macOS "installer" is really just a pretty Finder window that is presented from a read-oly DMG-based volume (that way, copying the .app out of the installer window always makes a copy). If you embed a different icon in each .app "flavor" the installer window should show the correct one.
If we want to provide a way for people to install release, alpha, and nightly apps side-by-side, then we do not need to do anything: macOS users already do this today by creating a folder for each copy of the application. The folder will then contain Tor Browser.app and the TorBrowser-Data folder that is associated with that instance.
On the other hand, if we want to allow users to put release, alpha, and nightly app bundles in /Applications all at the same time we would need to do two things:
(1) Use a unique name for the app bundle, e.g., Tor Browser Alpha.app vs. Tor Browser.app.
(2) Use a unique name for the TorBrowser-Data directory. Today when the application is launched from /Applications, the data directory is always created in the same location (~/Library/Application Support/Tor Browser-Data), and sharing that between release, alpha, and nightly could cause problems.
My opinion is that it is not worth the engineering effort to do (2), but maybe we should do (1). Having a unique .app name and icon would definitely make it easier for people to keep track of which app is which.