What are the Fourier-, Laplace- and Z-transforms of the impulse response of a filter called? I've seen $H(s)$ referred to as the system function or transfer function, what about $H(i\omega)$ and the discretized $H(z)$?
I would consider them to all be 'transfer' or 'system' functions. Those two names are interchangable, but in control theory books I see then listed more as transfer functions rather than system functions.
The domain you are in, whether it be fourier, laplace, Z or time, isn't entirely relevant to the name in that respect.