Pre-Crisis, the parasite was Maxwell Jensen. Post-Crisis, Rudy Jones. They were pretty much the same character in concept, except Rudy started life as (gasp!) a Firestorm villain, and was originally green and orange.
(The fact that he was a Firestorm villain of course meant he had to die messily at some point)
Anyway, Rudy absorbed various powers and got a shapechangers powers in some unrelated fashion, and decided that he'd get close to Supes by replacing Lois.
(This also apparently involved having sex with Lex Luthor. Not kidding)
At the end of that arc, Parasite died. Some time later there were a new set of Parasites, a female and a male twin. One was green and one was purple. The male one was killed off, but the female escaped.
And that's as far as I know what's going on with the various Parasites. It looks like the temporary shapechanging powers are part of his parcel now.