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If the definition of timezone names can change, then the combination of a future datetime and a timezone name does not identify a point in time.

Also, what if I don't know yet where I will be and I want to set a reminder for a particular date and time?

If I set my cellphone alarm to go off at 6am, and it goes off at 8am instead “because it's currently 6am in new york”, the alarm clock fucked up.

Unless New York gets split into two, Berlin-style, and the parts have different time zones.

Should it ring twice if you go across the border one way? Should it not ring if you go across the border the other way?

Yes? Same could be said right now for setting an alarm during the hour skipped/repeated by a DST transition.

You also need to record the offset with the datetime and time zone. Otherwise you won't be able to detect changes to time zone rules.