Rip Van Winkle had an identity crisis even before he went to sleep for 20 years. As a young man, he had "insuperable aversion to all kinds of profitable labor... Rip was ready to attend to anybody’s business but his own; but as to doing family duty, and keeping his farm in order, it was impossible."
This character flaw made him a favorite of all the people in his village but a real problem for his wife. He was known as a "henpecked" husband and caused a "fiery furnace of domestic tribulation". He simply was more of a romantic character who was content to watch the flowers grow rather than to cultivate and fertilize them. Once he wakes up, his wife is dead and he is able to live with his daughter. Without a farm to take care of allows him to be the "simple, good-natured man; he was" and his identity crisis is over.
Rip Van Winkle seems to have an identity crisis after he awakes in the woods. When Rip wakes up in the woods after what he thinks is a long night of drinking with the little man that he met on what he thinks was the previous night, he finds that his dog has run away and his gun is completely rusted over. He has no idea what is going on and at this point seems to begin to have an identity crisis. He actually fell asleep for twenty years but does not realize it until he goes back to his home village. When he gets there, he finds that most of the people that he once knew are dead, including his wife, the bar that he once frequented has now become a hotel, and the people are talking about things that he can not understand like the Revolutionary War. To top it all off, when he mentions his own name, Rip Van Winkle, the people direct him toward a man who looks just like him but it is his son. Since Rip is thrown into this new world overnight, he does seem to suffer from an identity crisis in the story.