I believe those are the initials, yes.

The "9" refers to the maximum number of "stages" which is not the same thing as the order of the solver.

The (m,k) refer to the corresponding parameters of the method (I think).

The "n" at the end is for "numerical" Jacobian (as opposed to "a" for user-provided/"analytical").

There should be a PDF in the download that explains these better than I possibly can (though it's still somewhat terse).

I had a look before asking but could not find anything before the download. Thanks, it piqued my curiosity (used to write & theoretically analyse several numerical integrators back in my teaching days)