Quantum spin is an intrinsic angular momentum of a particle. It's angular momentum that is 'just there' as a key component of the particle.
In early days it was hypothesised that particles were spinning about their own axes, but this isn't accurate.
All the interesting stuff of Spin from its quantizable nature, the non-commutatability of spin measurements along orthogonal directions, the very different fundamental behavior of particles with half-integer spin (Fermions, eg Electrons, Protons) vs integer spin (Bosons eg Photons), how Spins interact (eg spins of say two electrons with half-integer spin interacting as a Spin-0 Boson in a Cooper Pair of a superconductor), or spin interacting with orbital angular momentum eg electron spin interacting with it's orbit around proton in an atom.
At the end of the day Spin isn't a terrible name for it.
I believe Spinor vectors are merely named after the eigenvectors used to represent spin itself, not the other way around as you suggested.
I think we maybe saying the same thing (unless I'm not reading that right) - Spin is not named because it's physically spinning (ok intrinsically perhaps, but that still isn't intuitive to me) but because the way we measure its interactions it's easier to describe using Spinors?
In early days it was hypothesised that particles were spinning about their own axes, but this isn't accurate.
All the interesting stuff of Spin from its quantizable nature, the non-commutatability of spin measurements along orthogonal directions, the very different fundamental behavior of particles with half-integer spin (Fermions, eg Electrons, Protons) vs integer spin (Bosons eg Photons), how Spins interact (eg spins of say two electrons with half-integer spin interacting as a Spin-0 Boson in a Cooper Pair of a superconductor), or spin interacting with orbital angular momentum eg electron spin interacting with it's orbit around proton in an atom.
At the end of the day Spin isn't a terrible name for it.
I believe Spinor vectors are merely named after the eigenvectors used to represent spin itself, not the other way around as you suggested.