Actually it's Training Center Evaluator. They can only give rides as part of their 142 school program. The FAA has a list of DPEs but you have to go through it office by office, there's no search function by ratings given. And Air Crew Designees can only give rating as part of the airline training program they are linked to.
DPEs are more for planes like the CE500 series and old warbirds. Someone was looking for a 737 DPE a few years ago and I went through the whole list. Was surprised there was one. But as I recall there was only one transport jet DPE listed.
Plus for a type rating per 61.157 (b) you need to have a record of flight and ground training.