This is an excerpt from the above article on Wikipedia. Christopher Robin Milne is A. A. Milne's son, better known in the books as Christopher Robin...
Christopher Milne had named his toy bear after Winnie, a Canadian black bear he often saw at London Zoo, and "Pooh", a swan they had met while on holiday. The bear cub was purchased from a hunter for $20 by Canadian Lieutenant Harry Colebourn in White River, Ontario, Canada, while en route to England during the First World War. He named the bear "Winnie" after his adopted hometown in Winnipeg, Manitoba. "Winnie" was surreptitiously brought to England with her owner, and gained unofficial recognition as The Fort Garry Horse regimental mascot. Colebourn left Winnie at the London Zoo while he and his unit were in France; after the war she was officially donated to the zoo, as she had become a much-loved attraction there. Pooh the swan appears as a character in its own right in When We Were Very Young.
In the first chapter of Winnie-the-Pooh, Milne offers this explanation of why Winnie-the-Pooh is often called simply "Pooh":
But his arms were so stiff ... they stayed up straight in the air for more than a week, and whenever a fly came and settled on his nose he had to blow it off. And I think – but I am not sure – that that is why he is always called Pooh.