I always logged the type of sim (ex ATC920) and the location. Tribal knowledge was that this was an FAA requirement, and it does make sense so there's some accountability if anyone (the FAA) ever needs to go back and verify your history.
As others have said, sim time is not "flight time", which has an FAR definition requiring an aircraft that actually flies.
"Total Time" is defined by the FAA, it can be whatever you want it to be.
But be very careful mixing flight time with anything else. When employers (especially 121) ask about flight time or total time they mean actual aircraft. If you give them a number including sim time or any other non-flight time without calling that out they'll probably assume you're trying to pad your time. Buh-Bye!