Like anything in life it all depends on what you do and who you do it to.
If you shoot a gang member in downtown Detroit you might not even make the local news. People have made a bigger deal about a rapper saying they'll shoot someone than they do when someone actually gets shot. If you killed someone that is influential to a city or area, mayor, police chief, etc., your name would be brought up when it happened, when you get sentenced, and when you try to get parole or are put to death. If you do something along the lines of a mass shooting you'll be talked about on the big news stations and have people try to figure out why you did what you did. Depending on where you do it you might be brought up on the anniversary.
But, the only way that you could live in infamy is if you do something not done before. If you were to kill someone along the lines of a world leader or huge celebrity. John Wilks Booth, Mark David Chapman, Lee Harvey Oswald all killed people that many people loved. They killed people that made a huge impact on alot of people's lives. If someone kills someone that is known worldwide then thats a way to always be remembered.
Or if for one reason or another your story sticks w/ people, something that people have never thought of before and will never forget. Sure we could all name some famous serial killers, but mostly b/c they have been used as the centerpieces and influences for movies and classic characters. Norman Bates from Psycho, Texas Chainsaw Massacre, Hannibal Lector and Buffalo Bill from Silence of the Lambs and those are all take offs of Ed Gein. No one had heard a story like what Ed Gein had done before and when they heard that story it stuck with them. That story made enough impact on Alfred Hitchcock, Tobe Hooper, and so many others that they used bits and pieces of it to make some of the most classic horror stories and characters. We all know Jack the Ripper b/c he was the "first" serial killer and the Zodiac Killer b/c he did something that isn't supposed to happen, he didn't get caught. I know there are more but I think I made the point I was trying to make. There have been alot of serial killers, but if you ask anyone, an expert in the field or someone of the street, to name a famous serial killer I think that the same names will come up multiple times. The story needs to be memorable, and nothing is more memorable than something never done before.