Nope.
It's called a neutron star because a great portion of the star is believed to be composed of neutrons. There should also be a mix of protons and electrons as well, with a greater proportion of neutrons to other particles as you get closer to the core. (Because the pressure is higher near the core, which makes it more favorable for protons to combine with electrons and form neutrons)
Also, it is a misconception to say that 99.99% of everything is empty space. Fundamental particles are thought of as point-like, meaning they have no dimensions. Yet atoms still have "sizes" based on how the electrons occupy their states around the nucleus. It's actually kind of complicated, and you'd have to look into Quantum Mechanics a bit to understand it.