The record is in the company training records. I keep a record in my log, but as my logs don't usually go to recurrent training with me, the log gets filled out at home. To be an official log entry of simulator time, the entry must have an instructor's endorsement with it. As mine don't, and I don't believe in logging sim time for any purpose other than record keeping, each sim session gets a line entry in the logbook, but is never reflected in any total.
Simulator time isn't flight time, and shouldn't show up in your logbook as anything but simulator time. It doesn't show up as total time, multi engine time, or anything else, and in my logs, doesn't show up in any total.
The FAA recognizes it separately. In cases where sim time can be used toward the experience requirements of a certificate or rating, the sim time is counted separately. When filling out the FAA Form 8710, for example (application for a certificate or rating), one puts down the actual flight time. If Fifteen hundred hours of flight time is required toward the ATP certificate, for example, and one has used 50 hours of time time credited toward this requirement, one shows only 1,450 hours of flight time on the application...and 50 hours of sim. The FAA will do the math, but sim time isn't flight time and shouldn't be reflected as anything but sim.
So far as showing it as dual, you can (because by it's very nature, in order to be logged it must be dual), but I don't put any totals pertaining to the sim time at the bottom of the page. Further, in my logs, PIC time plus Dual plus SIC equals total time.