The rumours, which are complicated and require a full afternoon of web research, first started in 2004. In a nutshell, they claim that another person named Steev Mike was the original Andrew W.K., and that the current W.K. took over for him in 2005. It doesn't help that many of W.K.'s albums have listed Steev Mike as some sort of producer.
Regardless, Andrew W.K. has responded to the rumours numerous times. In an interview with British magazine Front back in May, he explained the situation, saying, "Steev Mike is the executive producer on my first album. The nature of how we presented my initial offerings caused some confusion, even though I tried to make it as straight forward as possible... Most of what you've heard is exaggerated but the parts that are true may be more disturbing than you'd hoped."
This weekend, W.K. was once again attacked with a barrage of private and public messages on his Twitter. He replied to them, saying, "To answer all the questions people sent: NO! Don't buy into this crap! They're just haters... The answer is NO! I am a real person, of course, and I didn't replace anyone or get hired by anyone in 2005 to take over Andrew W.K."
He attempted to end the barrage, saying, "Anyway, I'm going to stop talking about this because as usual it just doesn't make a difference. So you haters, you can just hate in peace!"
Even that didn't stop anything, so he added, "With all due respect, please stop sending me direct messages with questions about whether I'm a hired actor or my past. PARTY messages only!"
Finally, to shut down the accusations, W.K. finally posted four photos of himself taken in the early 2000s, thereby hoping to add further proof that he's the same person. The photos can be seen here.
While Andrew W.K. definitely pushed significant evidence that he's not an impostor, there's a good chance that this web of controversy has not gone away. If you want to read up on the conspiracy theory, an enormous amount of material is available here.