Do they have protons or only neutrons? because if there are no protons then it is technically just neutronium and not an element,

If they do have protons, then it is safe to assume it is a ridiculous number like 10^40. in which case I would count it as an element. And given how unlikely is for 2 neutron stars to share the number of protons, then every single neutron star is its own element,

And also, because they do not react with other atom, and if 2 collide then they merge their nucleus, we can agree that they are non reactive, and therefore we can consider them noble gasses…

Wait, are they gas?

YES, they are, if there is a single atom floating in space I think that counts as a gas