Good point.  When I wrote my Parinfo class (https://github.com/pyspeckit/pyspeckit/blob/master/pyspeckit/spectrum/parinfo.py), I set it to name each parameter with a trailing number, but that is more closely analogous to making `param_dims > 1`.  

Honestly, prepending the child model name, perhaps with added digits in case there are many identical children, seems like the best way to go to me.