You are correct. I should have said "a punishment"; however, even that would be technically incorrect.
But I guess what I mean is that the fame is pure karma which they shouldn't be allowed to rid themselves of because they committed murder. (I assume murder because "they were sentenced to life in prison.")
Apparently the dominant legal view in Germany (and I guess in more parts of Europe) is that once a sentence is served, the crime is dealt with. If society believes that the sentences are too light, it can change the law, but once a judge has pronounced a sentence, and it's served in the proper way, that's it.
"Fame" is a way of society to hand out punishments outside of the courts of law. Such an extrajudicial punishment is especially annoying when there are mitigating circumstances. Usually those are details that courts bother with, but public opinion doesn't.
(Now, that doesn't mean this particular case is easy. Wikipedia also records history. History records the identity of many killers and I believe in a lot of cases that can be an important historical fact. Balancing rights rarely is easy, so I'm happy that we have independent professionals that spent a lot of time thinking about these issues.)
But I guess what I mean is that the fame is pure karma which they shouldn't be allowed to rid themselves of because they committed murder. (I assume murder because "they were sentenced to life in prison.")