Probably been mentioned already (I'm always late to Star Wars threads), but wasn't there buzz about Obi-wan having a secret wife or something before TFA came out? Am I totally imagining this, or does it actually come from somewhere? (It may have also been Han Solo, I don't really remember)
If Obi-wan did have a relationship in the past, it could be his kid.
I don't think the timing works out to be Obi-wan's kid. Rey is 19 in the film, but the film is set 3 decades after ROTJ. Even Kylo Ren seems older than Rey and is certainly not around at the time of ROTJ. But Ben Kenobi had already been dead for several years.
I mean, it's possible that there was some genetic material stolen from Ben.. but how? The Empire didn't seem to know where he was; and his body completely disappeared after his death. Even if there skin cells on the Death Star, it died pretty quickly.
PERHAPS Obi-wan's grand-daughter. But the connection then becomes very tenuous -- we would never know her grand mother and the parents also become unclear. And it certainly wasn't hinted at in TFA.
Occam's razor suggests it will be Han / Leia, because Leia hugged Rey really tight and because Han said "there was something about her". It might even be the reason why Han and Leia didn't work out (Their kid was abducted. Han goes searching the galaxy for her, but never finds her. The distance makes things tough. Kylo Ren grows up without a father figure as a result, which causes him to idolize grandpa Vader.)
The only other option in TFA would be Luke. I do think that's a big possibility. Because Luke will die in the next few films (probably TLJ, maybe the finale) or else the next generation is not able to inherit the mantle. Just like Obi-Wan and Yoda needed to die. And once Luke dies, the skywalker family tree shrinks quite a bit with only Kylo Ren left.