Some 100 years ago, the 32nd President of the United States, Theodore Roosevelt, went on a bear hunt. He enjoyed nature and being out in the woods where animals lived. Because he was the President of the United States, the people organising the hunt wanted to make sure the hunt was successful.
But after 3 days of walking and climbing and riding, no bears were found. Now what? The President's bear hunt would be a failure!
The next day, the hunt guide and his hunting dogs finally found an old bear. The dogs and guide followed the bear for quite a distance until the bear was very, very tired. The dogs attacked and injured the old bear. The guides tied the bear to a tree and called for the President. Here was a bear for him to shoot.
President Roosevelt looked at the poor old bear and said "no!" No one would shoot this old bear for sport. That would not be right. However, the bear was injured and suffering. President Roosevelt ordered that the bear be put down to end its pain.
Afterwards, a political cartoonist by the name, Clifford Berryman, heard the story and drew a cartoon showing how President Roosevelt refused to shoot the bear while hunting in Mississippi. Thus, the cute bear cub began to appear in other cartoons which Berryman drew throughout Theodore Roosevelt's career. That, in a nutshell, was how a bear became connected to the name of President Roosevelt.
But after the famous cartoon appeared in the papers, a shopkeeper, Morris Michtom, took two stuffed toy bears which his wife had made and put them in his shop window. He obviously had an idea. Mr. Michtom asked for permission from President Roosevelt to call the toy bears "Teddy's bears".
This store eventually became the Ideal Novelty and Toy Company. Thereafter, the phrase caught on and toy bears were since then called teddy bears!
Source: Theodore Roosevelt Association