Litvinenko? Putin was definitely aware of him - he was an FSB guy who went public with a scandal about FSB members being hired out by organized crime in the late 1990s. This included, supposedly, an order to kill Berezovsky, and he went public in a press conference in 1998. He was fired as a result by Putin acting as head of the FSB. Then he went to Britain and claimed asylum, after which he worked with MI6 and made public claims about the Russian power structure, some of which were bizarre and certainly not true (e.g. that the riots about the Muhammad cartoon in a Danish newspaper were orchestrated by the FSB to punish Denmark for its refusal to extradite Chechen separatists).I bet Putin was unaware of this guy's existence, before he died. Like ~99.999% of other people.
His public denunciation of the FSB, repeated loudly after his asylum in the UK, and work with MI6 definitely gave the FSB a reason to want him to die in a slow, public way as a warning to anyone who might try defecting in that manner. He also appears to have pissed off some organized criminals as well, so it isn't totally impossible that it could have been organized crime rather than the FSB. And of course it's also quite possible that the FSB did it without a direct order from Putin. But the circumstantial evidence definitely points to the FSB, with Putin either ordering the hit or providing implicit support to the assassination while not specifically ordering them to kill him.
https://en.wikipedia.org/wiki/Alexander_Litvinenko