Inconsistency in default classical register names

[wshanks]

With the SamplerV2 using the names of classical registers as part of structure for storing results, classical register names have become more important than they were in the past with qiskit.result.Result which just put all the registers together. So

circ = QuantumCircuit(1, 1)
circ.measure(0, 0)

stores a result in classical register c while

circ = QuantumCircuit(1)
circ.measure_all()

stores a result in classical register meas and

circ = QuantumCircuit(1)
circ.measure_active()

stores a result in classical register measure.

I think ideally all three patterns would store into the same classical register name by default.

Given that the current behavior has existed for a while, I think it might be too hard to change it now, but I wanted to capture it at least. The defaults could be migrated to a common name, but in the transition period users would need to be more explicit about register names (since I think the way to do it is keep the old default but issue a warning that the default will change, so users would need to start passing the new default explicitly to prepare for it) and once everyone is being explicit it might not be worth trying to let people be more lazy by using the new common default name.

[1ucian0]

As per discussion in #12345 (comment) , I think changing the default names should be consider a breaking change and, therefore, for the next major release (2.0). Adding it into the 2.0 milestone.