I'm looking for a word or phrase

[SheilaT]

6. Again, not one word,

but "self-fulfilling prophecy" is a cousin to what you want.

If people get treated as if one aspect of them defines their entire self and is used to predict their future, you sometimes get a self-fulfilling prophecy.

I'm also curious if you're only thinking about the negative aspects. There can be positive ones, also. But the positive side can also include overreach, such as if you assume someone who is good at one thing, like managing a pet store, would be equally good at something similar, such as managing a water park or running an entire empire of food stores there can be problems.