How to distinguish the type of transistor amplifier
Looking for a mnemonic or some mental hack to distinguish different transistor circuit configurations is the wrong thing to do.  Think about it.  What would be the point?  The purpose of naming some common transistor circuits is to quickly communicate them to others, and after some experience, to short-cut some analysis of the circuits.  Simply being able to name a circuit without understanding what that means is pointless.  Teaching students to do that is doing them a disservice.

Instead, they should learn some basics of how bipolar transistors work, and then how they can be used in some common circuits to achieve certain goals.  There is no substitute for actually understanding these things.  The fact that some of these circuits are common enough to have standards names should only be a minor point once the understanding has occurred.  After the students work with these common circuits enough, they'll eventually remember their names.

Learning by memorizing mnemonics and half-baked rules of thumb is no learning at all.  Do your job right and teach them what they really need to learn.