I know not your area, but after having worked in a couple shops, here is how to decide, in part -
Look around the shop itself. Is it organised and clean? Not just the lobby, but the work areas where they rebuild and where they do the removal/installation.
The way they take care of the shop is a direct reflection of the kind of work they do.
The name itself does not mean a whole lot. I have worked at two AAMCO'*.
AAMCO is suppose to be the first name in transmission repair, but :
One was a **** pit, and the work done was poor.
One was cleaner than MArtha Stewarts house, and the work was excellent.
Ask them if they rebuild with new parts or used. At the crap shop I was at, we just used hard parts off of junk tranny'*.
You want new parts.
1999 LeSabre, 3800 series II engine.