Episode #359 of the Let's Talk Bitcoin! podcast — my favorite cryptocurrency-related podcast — was released yesterday (2018-03-11). It was a conversation between Stephanie Murphy, 
From Adam:
Every now and then I get emails from people who say they are Satoshi. And I once had Satoshi buy me dinner in Nashville. I have a good relationship with Satoshi. ... In the last two weeks, I was contacted by, a very, not necessarily convincing, but a very detail-oriented Satoshi, who is getting ready to release a book about how Satoshi created Bitcoin.
However, this satoshi couldn't provide cryptographic evidence that he possessed private keys believed to have been created by Satoshi. Adam was thus immediately skeptical:
Satoshi set it up in such a way so that if Satoshi were to come back it would be basically impossible to tell unless he could do certain cryptographic things, which so far no one has been able to do.
It's worth noting that having Satoshi's keys doesn't necessarily prove someone is Satoshi (although it would be more plausible). However, if Satoshi deleted his private keys, then he made an irrevocable decision to never be able to cryptographically assert his identity as Satoshi. I think this is highly probable as the keys would be a liability for remaining anonymous.
Adam continues with the story of the fresh fake Satoshis:
I had a Satoshi reach out to me, who said that he was writing a book. And I was like alright prove you're Satoshi to me. Sign something with a Satoshi key. And he was like, "yeah, I can't do that, but take a look at this narrative". And so I read this narrative and it's from this developer who claims that he's one third of the satoshi pair with Craig Wright and Dave Kleiman being the other ones. … I get to the end of the narrative and I find this one part I really can fact check, which is a connection to Zachtronics Games. And I contact the founder of Zachtronics Games and he's like this is nonsense … so I reach out to this Satoshi... and he tells me that actually this isn't his story. That that story was written by someone else who's claiming to be Satoshi, incorrectly, and that person accessed Satoshi's emails and used those emails to reverse engineer … all of this stuff.
Adam nicknames these two new imposters as Scrontee and Fauxtoshi.
Craig Wright
The podcast briefly discusses an ongoing Satoshi imposter, Craig Wright. From
Craig Wright did produce proof and it was forged. The only proof he produced was a fraud.
You can read more about Craig Wright's misleading claim of Satoshi's signature in Craig Wright's New Evidence That He Is Satoshi Nakamoto Is Worthless. My favorite quick from that article is from Peter Todd:
It would be like if I was trying to prove that I was George Washington and to do that provided a photocopy of the constitution and said, look, I have George Washington's signature.
What motivates fake Satoshi's?
Recently, Dave Kleiman's estate has sued Craig Wright, seeking 1,100,111 BTC. So claiming he was Satoshi really backfired for Craig Wright. Adam speculates fake Satoshi's may be motivated by increasing their credibility (perhaps as marketing for a book or ICO scam).
This behavior craves the attention, even the negative attention that declares them to be lairs and frauds. That drives it even more than the possibility of profit. This is the expression of mental illness in a public forum.