It depends on how you want to interpret "yourself". Our selves have very many facets. We have the at-home facet, the with-friends, the one at-work, the one in front of a court. They are all our self. It basically means be natural for the face you're putting on. Don't over do it. Don't construct something overly elaborate such that it misrepresents you and it becomes apparent. Don't over think it.
I don't have a "write some algorithm in 15 minutes" self because I never do it at my job, but here I am, trying to rush an implementation on a whiteboard.
Part of that is doing research and getting to know what the company looks for in candidates and what you can expect in interviews and how you meet them. Sometimes it won't be a good fit, and that's alright.
If they want you to be their monkey and that's not you, I'd say don't do it. Of course, that's very easy for me to say, but if you think it's unreasonable and don't like it, find another company. There is no "one" company --just like there is no "one" romantic partner. It's all about trade-offs.
