Two paying customers will travel to the "deep space" beyond the Moon. SpaceX will use the Falcon Heavy to deliver an automated Crew Dragon capsule carrying the unnamed customers next year. Falcon Heavy has not flown yet, and is expected to be tested this summer. NASA will use the Crew Dragon capsule to send astronauts to the International Space Station in 2018, after an unmanned test this year.
SpaceX will not reveal the identities of the participants until they complete health and fitness tests:
We are excited to announce that SpaceX has been approached to fly two private citizens on a trip around the moon late next year. They have already paid a significant deposit to do a moon mission. Like the Apollo astronauts before them, these individuals will travel into space carrying the hopes and dreams of all humankind, driven by the universal human spirit of exploration. We expect to conduct health and fitness tests, as well as begin initial training later this year. Other flight teams have also expressed strong interest and we expect more to follow. Additional information will be released about the flight teams, contingent upon their approval and confirmation of the health and fitness test results.
Two random venture capital names in Silicon Valley that nobody's heard of.
I think your serious guess might not be so serious, but commenting on it: Musk has repeatedly expressed aversion to being one of the first to actually do somewhat risky things until SpaceX has reached its goal which is human settlement with supply ships playing back and forth from there and Earth. I put the chances of one of them being musk at just about 0. And Bezos similarly has shown a huge degree of envy and what seems to be jealousy of SpaceX's success relative to Blue Origin. I think there's 0 chance he'd be willing to go on, let alone pay for at large personal expense, a somewhat risky flight that will cement SpaceX's place in the history books.
Actually, I think there is one person I could name (and many people have heard of) - Steve Jurvetson. He came to mind immediately. Checking his twitter, it was kind of interesting that he made a slightly out of character post about getting egged into skiing a double black diamond for the first time ever literally just an hour or two before SpaceX's announcement. Probably just a funny coincidence, but adds a tiny bit more salt to a name I would probably have already picked.