you should recognize the foliage, if nothing else
This doesn't help, since many plants have identical foliage, while other plants have several different configurations of the same foliage, making it just a bit of a pain to identify identical species.
i suspect it would have been a pain in the patootie to code the game so that it told you what kind of plant was growing before it was mature...
I used to work on an MMORPG, and it was very simple to code this. All it required was a yes/no flag for the player. So: player A has produced a Fabled Fern. As soon as that occurs, the game trips the flag in the database next to Fabled Fern, and the next time a Fabled Fern is planted--which can only result from a certain combination of parents--the flag is read, and the game states the plant name above it.
That's not to say it would be easy to code in PT, only that it can be done with ease in some games.