In the first chapter of the book Winnie-the-Pooh, A.A. Milne writes the following as to why the name is officially "Winnie-ther-Pooh" (though Milne never calls him that again anywhere in the stories):

When I first heard his name, I said, just as you are going to say, "But I thought he was a boy?"

"So did I," said Christopher Robin.

"Then you can't call him Winnie?"

"I don't."

"But you said---"

"He's Winnie-ther-Pooh. Don't you know what 'ther' means?"

"Ah, yes, now I do," I said quickly; and I hope you do too, because it is all the explanation you are going to get.