I finally find out the pattern! I tested with an iPhone operating at iOS 14.4.
In iOS 14.4, the ad tracking authorization dialog is only shown for the first time it is installed/requested. Even you uninstall and reinstall the app, iOS would not show the dialog again and return the previous value chosen by the user, i.e. "authorized" or "denied".
You can test it by changing the bundle id to any other value. The authorization dialog can then be shown again!
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This is a flow chart to better present the way for changing the "app name" shown on the "Apple ID logins" on the Settings page.