The spell clearly says that it does not affect a shapechanger.
Shapechangers are not affected by this spell.
But has nothing about the opposite.
Would that mean that I can change a Goblin into a Doppelganger and that Doppelganger cannot then ever be transformed again with a True Polymorph spell?
Best Answer
The spell description doesn't say you can't
Preface: You cannot true polymorph a Goblin into a Doppelganger.
From the spell description. (Goblin is a CR 1/4 creature).
Discussion
If you chose a CR 3 creature like a Killer Whale, the spell's language indicates that it is the new creature: a Doppelganger. (Likely one with a taste for raw herring). Why? Nothing in the spell description says that you can't.
The Fine Print
There's some fine print to consider (at least in the SRD version of True Polymorph, p. 188).
The "full duration" refers to the hour of concentration it takes to make the true polymorph permanent. That true polymorph is "until dispelled" is shown in the SRD and in editions of the PHB after the first one was issued.
Its true form is now a Doppelganger, not a Killer Whale. It can't change back into its old form to go hang out with its orca friends (It could have done that had it originally been a CR 3 humanoid, for example a Hobgoblin Captain). Might the Doppelganger want to return to being a Killer Whale?
If someone knows that the Doppelganger was originally a Killer Whale and wants to return it to that form, or if the now-Doppelganger encounters an effect that dispels magic, then this subsequent dispelling returns it to Killer Whale form by either a friendly or hostile action.
Is that really a prince inside that frog?
This raises the in-game question of "Why would he want to be a Killer Whale again?" (Beyond the obvious case of his agent wanting him to star in Free Willy 5: the money's too good!) That's up to the DM to decide based on the story and motivations of the NPC's and monsters under his control. Something about the smell of fresh herring, down by the docks at midnight, awakens a yearning deep in the Doppelgangers heart ...
In that case, convincing someone to cast another true polymorph would be wasted effort, and would not make the change per the rule you cited. A dispel magic spell could if the DC check is successful, and a dispel magic spell would if it is cast from a 9th level spell slot.
Dispel Magic(p. 136)
There's another way that the Doppelganger would revert (at least for a while) to its original Killer Whale form: it encounters an antimagic field.
Antimagic field lasts for up to an hour. Will the Killer Whale survive for an hour if the antimagic field is not encountered in the water? That depends on the situation, and might be the core plot hook for Free Willy 6!