Is it possible neutron stars are actual elements? As you go up the periodic table (more protons), the ratio of neutrons to protons steadily increases as well. Are we sure there are absolutely no protons and electrons in a neutron star, or could there be so much more neutrons that we cannot measure any protons and electrons? Perhaps then a neutron star is a nucleus of some huge element with a neutron:proton ratio higher than we can distinguish.
To be considered an element, they would have to have a positively charged nucleus. They don't. The neutron star is largely neutral.

They would have to have a cloud of surrounding electrons. These electrons would have to share "orbitals" with other electrons around other, nearby neutron stars. That doesn't happen.

Finally, at these scales, gravitational interaction predominates. Even if neutron stars did have some positive charge, and did have electrons orbiting them, interaction with other neutron stars would still depend a lot on gravity.

Finally, even if a neutron star was charged, it's not clear whether electrons around them would actually fall into some kind of orbitals governed by quantum mechanics. QM tends to not happen at such a scale.

In conclusion, no, they are completely unlike atoms and their nuclei.