I think we've always been pretty loose about how that is used. For example, I have never officially represented the IEEE but I am always listed as IEEE in the minutes.
Part of the reason I haven't done what you suggest is that I don't always know from year to year who is a representative and how isn't. Also, sometimes a person might be acting as a representative in the context of an agenda item and as an officer in another.
My suggestion is that I could put a column in the attendance sheet that lets you check off if you are a PSEC Representative and I can add that to the minutes. Does that sound like a good idea?