Really not clear what you're actually asking.
From your profile you have a PPL, which would imply you are on about demo flights with a view to buying the aircraft, in which case you wouldn't be offered a flight unless you were pretty serious about buying, and then you would be free to fly the thing, check slow flying/stall characteristics, and any other general handling items which would be relevant to ownership of the aircraft. If you're just looking to get some time, not sure who will be offering such flights, and I don't see you would be able to log this.
If you're looking to experience flying other aircraft, and are actually on about flying with an instructor, this would be perfectly standard on a type you have not flown, and you could log the time as P U/T. If your club has other aircraft you have not flown, it would typically be a "check out" with an instructor. Depending on your experience it would be an hour or two covering everything from General Handling, PFL, and landings to make sure you are happy with the aircraft before you go off on your own.
In either case, I cannot see anyone "showing off" but any pilot would be trying to demonstrate what the aircraft is capable of.