I think I have remembered this correctly.In one of the AA Milne books, the reason is given that Christopher Robin used to go and feed swans, one of them was particularly intimidating as swans are and to show that he was not frightened of the swan, Christopher Robin used to say "Pooh" to it (in the context of "pooh-poohing" something, not the bodily function).
During WW! troops from Winniepeg were going to Canada. On route the train stopped at White River. LT. Harry Colebourn bought a small black female bear for $20. and named it after their hometown Winniepeg Winnie for short. Winnie became their mascot and went to Britain with the troops Harry Colebourn gave winnie to the London Zoo for long loan fron 19119-1934. Christopher Robin son of author A.A. Milne loved the bear at the zoo and it became his fav. animal there. He renamed his teddy Edward Bear Winnie. And then His father began to write about winnie and christopher. Pooh originally belonged to Swans and can be seen in Milne's intro to 'when we were very young'. Hope this helps I lurrve Pooh.
eh? dunno about the other responses but if you read the book it explains why - in the first story (forget the name) in which Pooh tries to get the honey/hunny out of the tree full of bees, he uses a balloon to float up to the trees. Anyway to cut a long story short after he comes back down he finds that cos he was in the air so long his arms are stuck in the air above his head and won't return to their original place for a few days. Therefore the name Pooh comes from the noise he makes blowing flies off his nose. Its true! - read the book
I agree with Trinity although I didn't know all the details, but when I went to London Zoo last year, in a souvenier booklet, they had a picture of the bear named Winnie, and had written that it inspired the character Winne the Pooh.