How to create Non-Central Student's T distribution and what priors to use with the distribution?

To simply get the variable names you can use trace.varnames

For diagnostics it’s best to use the library ArviZ.

import arviz as az
.....

    trace = pm.sample()
    idata = az.from_pymc3(trace)

then you can use the many useful functions from ArviZ such as, az.plot_trace(), az.summary(), az.plot_posterior()