The show hints at it the entire way through. That Klingon woman comes back to him early on and tells him she's has a way to make sure they can hurt the federation but it's going to require him to give up everything. He then vanishes and is never seen again. Then Tyler arrives pretty much immediately from nowhere, he even makes a comment at one point 'I miss having thicker skin' which is probably the writers making a joke about him having been Klingon, since he apparently doesn't remember anything. Then the Klingon woman (L'Rell) is shocked to see him on the Klingon ship at the end, he starts getting memories of her slicing him up. They have an entire scene with the doctor where he tells him that all of his bone structure has been completely changed, yet he still looks like a normal human. If I rearranged all of your bone structure then you wouldn't look human anymore. Hinting at him being changed from Klingon to human. She triggers him with a chant and he goes into his daze and starts repeating Klingon back to her in Voq's voice. She then says 'you have another name, say it' so it's painfully obvious at this point that he isn't Tyler, he's somebody else. The doctor then has a scene with him where he explains how it's possible he has another personality (Tyler's) on top of his own (Voq's) and then we get flashbacks of them both having sex.
At this point, any other reveal that he's really just some random Klingon or some other random human we haven't met yet would be completely pointless and the audience wouldn't have any connection to them enough to care. Plus Voq disappears and Tyler appears immediately after she tells him that she has a way they can get back at the federation but it requires him to give up everything. They go out of their way to spell it out so it won't come as a surprise, they could a.) have hidden it better and b.) built Voq up more because right now he's just a little bitch that had his ship taken away by someone who gave his crew food. Why should we care about him. Plus this plot has been done already in the original series on the episode The Trouble with Tribbles.