About the river of passion part, or about the name? If we're voting, I'm going to say yes to the first, maybe to the last. (I could easily hear Piggy's mother calling, "Pigathius! What do you think you're doing?"
But about the age part. Well, Kermit is older, but I would say that during TMS days, she was probably in her late 20s. She was very young and un-sophisticated at the beginning, but as she matures as a performer both her behavior and her look acquire great sophistication. Take a quick peek at clips from the first season, then the last season. Quelle difference! I would guess she ended her run on TMS in her early 30s, the age at which women actually begin to be intersting as women instead of young women.
Once, Gene Shalit suggested that she was aging remarkably well, and asked her if she'd "had work done," or at least implied it. The end result of that was probably Gene needed to have "work done." I would imagine that Piggy and Kermit will probably never "age" much beyond the mid-thirties to mid-forties range in terms of behavior. We're never going to hear about Kermit having a mid-life crisis (unless it's in fanfic) and Piggy will never relinquish her "Babe" status. (Hmmm..has a funny thought about the movie...doesn't say it for fear of being karate chopped!)