If the converter is slipping in lockup or not locking up you will have a code in the system, usually a P1728, but there are a few other codes related to torque converter clutch performance, it may or may not throw a CEL
The advantage to a triple disc converter is more holding power when the converter is locked up, most 4R100
converters anymore are either single disc billet, or triple disc billet converters, some companies might still make a 2 disc converter but I don't know of anyone who uses them. Usually triple disc converters are only used for vehicles that tow on a regular basis and/or are putting out a lot of torque, much more than stock.
Slipping is a generic term that doesn't mean much to a transmission tech, do the rpms go up between shifts ? do the shifts feel firm and positive, or do they drag out ? torque converter lockup should happen sometime after second gear, and should drop the rpms roughly 400-500 rpms,
I would pull codes first, and even if no codes, take the truck back to the shop that did the work, tell them your concerns and let them check it.