I don't see how anyone except John Oliver could fill in for John Stewart. Oliver is funny, he's enjoyable to watch, he's political, and the key thing is, he's earnest. Jessica Williams is a name that comes up a lot, and as great as she is, she doesn't have that earnestness that Oliver does, and she doesn't seem to get fired up about issues the same way that Oliver does, or Stewart did. I'd watch a comedy show with Jessica Williams but I don't think she's quite right to head up the Daily Show. She's one of the newer members as well; that may be why Comedy Central didn't give her the Colbert slot. Samantha Bee and Jason Jones? No way in hell that will happen. Samantha's OK but Jason has a grating presence- he pretends to be a dick but when he does, he comes across as actually being a dick. He's got that small, mean laughing-at-you-not-with-you thing that kept Craig Kilbourne from ever going anywhere with the show. Comedy Central clearly feels the same way: he was passed over to fill in for Stewart, and for Colbert's slot. I don't see Larry Wilmore happening either, he seems more annoying than funny and there's just a limit to how much humor about race a largely white audience can handle.
Everybody saw what happened when Oliver took over the Daily Show. Stewart was clearly looking to do other things. Even before this he's seemed worn out and ground-down, he joked a lot about how old he felt, at times he seemed to be going through the motions to manufacture his indignance- I think that's why he bonded with O'Reilly, John Stewart had become a lot like O'Reilly, someone who was paid to go on and pretend to be upset when he'd gotten to the point that he didn't really care that much anymore. And then John Oliver came on and for the first time in years, I actually thought that Daily Show actually was a fun show to watch. And everybody clearly saw that Oliver had that rare talent where you can get him up in front of millions of people, talk about the news, and people laugh and enjoy themselves. HBO saw it and gave him a show and he's proven he's able to headline a show, hell he can even turn net neutrality into comedy.
That's what you want. You want a guy who's funny, who's enjoyable to watch, and can make something as dull as net neutrality funny, and can get fired up about the politics: he actually cares. He's proven that he's all of those things, and none of the other names have. Oliver has the HBO thing, but my guess is that Oliver's agent negotiated some kind of a loophole with HBO so that he could go back to Comedy Central if asked. And the Daily Show is Comedy Central's flagship program. There's no way that they will replace Stewart with an unproven or unknown talent; they have too much at stake to take a chance and gamble with an unknown when they've got a proven talent who can not only do the job that Stewart does, but do it better than Stewart himself. The fact that they haven't named a replacement suggests to me that the deal isn't final, but I'm guessing that Comedy Central is currently in negotiations with Oliver.