In the launchd.plist manpage of Ventura I discovered that there is a new AssociatedBundleIdentifiers option. After I added the new option to our Agents and Daemon property lists the Login Items UI of System Settings still continues to show our Developer Program name instead of the name of our Application name.
AssociatedBundleIdentifiers <string or array of string>
This optional key indicates which bundles are associated with this job in the System Settings Login Items UI. If an app installs a legacy plist the plist should include this
key with a value of the app's bundle identifier.