I personally don't like seeing "Jr" on any name. The current naming scheme and how people are used to seeing them don't really fit well with suffixes like "Jr".
On top of that, when referring to a person with a "Jr" in their name, you almost always have to qualify who it is you are referring to. It just makes for confusing conversation sometimes.
More importantly, each person is really unique. Even each person in a twin pair or triplet group, are unique from each other in terms of inner character. Since no two person are the same, wouldn't it seem that a unique name would be appropriate to match?
Hey, I just answered a question with another questions!