Matlab can identify the current worker id with get(getCurrentTask(), 'ID'). While Octave does not even natively support parallel computing, the parallel package offers some parallel capabilities, but does not support labindex. So, I hacked my own solution (that currently only works on Linux).

tl;dr: give me the code

My oct_labindex package consists of the following pieces:

• An init function that shuts down all workers and re-starts them. Additionally, the file /<tmp-dir>/<pid>/child_pids is created.
• When restarting a worker, the parallel package always runs the ~/.octaverc file. The init_worker function must be called from ~/.octaverc. It checks if the command line of its parent proces starts with octave. If so, it assumes it is a parallel worker started by the parallel package and adds its own pid to the /<tmp-dir>/<pid>/child_pids file.
• The get_labindex function reads the /<tmp-dir>/<parent-id>/child_pids file and searches for its pid. The row index (starting from one) of the matching pid is returned as the labindex.

To use it, add the oct_labindex.init_worker() call to your ~/.octaverc startup file, load the parallel package, call oct_labindex.init() and run a parallel function:

% For proper usage, obviously add the functions to your path.
% Call `oct_labindex.init_worker()` from your `~/.octaverc` startup file
cd src
pkg('load', 'parallel');
n_workers = 2;
oct_labindex.init(n_workers);
pararrayfun(n_workers, @() disp(oct_labindex.get_labindex()), 1:10)

which returns the labindex for each evaluation:

 1
 2
 1
 2
 1
 2
 1
 2
 1
 2