Edward Bear is the bearâs formal name - Teddy Bear is his nickname, since Teddy can be short for Edward. Christopher Robin then gave him a second name. He is called Pooh after a swan*, Winnie after an actual historical bear, and âtherâ to apparently make it masculine.
Introduction to Winnie-the-Pooh (1926):
If you happen to have read another book about Christopher Robin, you may remember that he once had a swan (or the swan had Christopher Robin, I donât know which), and that he used to call this swan Pooh. That was a long time ago, and when we said good-bye, we took the name with us, as we didnât think the swan would want it any more. Well, when Edward Bear said that he would like an exciting name all to himself, Christopher Robin said at once, without stopping to think, that he was Winnie-the-Pooh. And he was. So, as I have explained the Pooh part, I will now explain the rest of itâŚ
âWinnieâ comes from the historical bear, above. She was an orphaned female bear from Canada who was brought to England by a Canadian soldier who arrived to fight in World War 1. He named her âWinnipegâ after his home province. Winnipeg moved to the London Zoo, where she was famous and beloved, and Christopher Robin admired her very much as a boy.
Then you put it together, in Chapter 1:
Here is Edward Bear, coming downstairs now, bump, bump, bump, on the back of his head, behind Christopher Robin. It is, as far as he knows, the only
way of coming downstairs, but sometimes he feels that there really is another way, if only he could stop bumping for a moment and think of it. And then he feels that perhaps there isnât. Anyhow, here he is at the bottom,
and ready to be introduced to you. Winnie-the-Pooh.Â
When I first heard his name, I said, just as you are going to say, âBut I thought he was a boy?â
 'So did I,â said Christopher Robin.
 'Then you canât call him Winnie?â
âHeâs Winnie-ther-Pooh. Donât you know what âtherâ means?âÂ
âAh, yes, now I do,â I said quickly; and I hope you do too, because it is all the explanation you are going to get.Â
donât you know what âtherâ means
and that is why Edward Bear is called Winnie-the-Pooh. And people just donât question it. Itâs just accepted.
* As explained in âWhen We Were Very Youngâ :Â âChristopher Robin, who feeds this swan in the mornings, has given him the name of âPooh.â This is a very fine name for a swan, because, if you call him and he doesnât come (which is a thing swans are good at), then you can pretend that you were just saying âPooh!â to show him how little you wanted him.ââ