What abbreviations, letters, or symbols do we use to denote highly degenerate stars? We have OBAFGKM to denote the strength of hydrogen lines.

Apparently we added S, N, C, and the W classes when we learned of new kinds of stars.

We use T, L, and Y to denote brown dwarfs.

The D classes refer to electron-degenerate stars (white dwarfs).

I've looked around quite a bit and I haven't seen anything regarding neutron stars and black holes. Does this mean there's no common symbol or abbreviation? What do they use in star catalogs? (I've never found a catalog with stars of all degeneracies in it.)
Neutron stars and black holes do not have assigned spectral types since they do not have a measurable optical/IR spectrum - which is the basis for assigning a spectral type.

There are many classifications for systems containing black holes and neutron stars. They are not related to the letter-based spectral types of "normal" stars or white dwarfs, but more to do with their X-ray, radio or inferred physical properties (e.g low- or high-mass X-ray binary systems).