There are no "atoms" in neutron stars. The density and temperature are so high that they are "crushed" and that the electrons and protons form neutrons. The result is tightly packed neutrons, hence the name.

I believe it is theorised that it might be possible to go even one step further to a "quark star" since neutrons are not elementary but made of quarks. No idea what a black hole might look like with no singularity...