Naming convention between two pins Input -> Output
You usually give a name that applies to the output signal because it is dominant and, the input has no play in how that signal is created or changes. You should also try and give the signal a name that is more applicable to what it represents and not what IC generated it so "SHIFT_REGISTER_1_OUT" is a poor name because it is meaningless.

If that pin is the really representing an input from say a tacho or microphone then it should have a name that encapsulates the original source meaning (if you can).

But, at the end of the day, it's up to you and nobody's going to get bent out of shape whatever you call it.