Welcome to SE Philosophy!
This is what is known in philosophy as a question of identity and is related to the metaphysical discipline of ontology, or the study of what is. In essence, identity is the question of what 'is' is, and is a source of much debate. Are equality and equivalence the same thing?.
Questions of identity related to personhood and the self are addressed in these SE posts.
Questions related to things that change over time are frequently tied to the Ship of Theseus and is old indeed. To wit:
In the metaphysics of identity, the ship of Theseus is a thought experiment that raises the question of whether an object that has had all of its components replaced remains fundamentally the same object. The concept is one of the oldest in Western philosophy, having been discussed by the likes of Heraclitus and Plato by ca. 500-400 BCE.
Note that this isn't really a question of biology, because if a fish becomes a polyp and returns to being a fish, biologists agree it is the same organism. But, are things that change really the same if they become different? With the Ship of Theseus, there are four general responses: yes, no, depends, and it's a meaningless question. That's the universal tell that any answer you get is going to be a result of your metaphysical presuppositions.
This is an interesting question because it is the ship-of-theseus problem in the guise of debate over the nature of biological immortality in the animal kingdom. From an analytically philosophical standpoint, the answer of the question is yes, because it follows from the definition of organisms which is a category which fundamentally accepts the change in state from birth to death. (Biologists would be in trouble linguistically if they had to classify that same living things as different organisms depending on development since there are no clear categories.) In the ship-of-theseus problem, it is less clear because objects are not defined so narrowly in such a way.