Reminyl, Aricept and Exelon all work in the same basic way, although as has been said Reminyl contains an extra drug as well. But they all have very similar actions and the aim is to increase the level of neurotransmitters.
AFAIK Aricept is the usual "first choice" because it is generally better tolerated with less risk of side-effects than the other two.
In all cases they will start on smaller doses and build up to larger ones (which is called "titration" I believe). This reduces the risk of side-effects and minimises them if they occur, and if necessary the drug can be stopped.
When Dad started Aricept he started with 4 weeks on 5mg and then moved to 10mg after.
With Exelon, which he is now taking, the build-up has been much slower, starting with only 3mg a day and increasing by 1.5mg every to weeks and we still haven't reached the full 12mg daily! This is because Exelon carries the highest risk of side-effects and we were told "if they happen they can be very nasty".
Your Dad may have been given Reminyl for a variety of reasons, his condition, the experience of the consultant, fitting in with any medications, etc.
My Dad was switched to Exelon because it is, apparently, more helpful for patients with "psychotic" symptoms.