I have my right-hand ring glamoured as the House Fortemps signet ring on everything.
More generally though, the glamour dresser does make it a lot more practical to glamour jewellery consistently, so it's likely that some people do glamour specific rings.
It's unlikely that they would split rings into Left and Right, because they would actually needed to be coded separately (and duplicated if you want to wear the same ring on both hands). It would be the same kind of issue that prevents us from glamouring mages' wands over staffs - they're classified as different item types. If rings were split, you couldn't just have two identical rings any more, you'd need two unique items coded for the correct hand.
It would almost certainly cause more issues than it solves.