The Anansi stories originated from Ghana’s Ashanti tribe.
There is an Anansi story that explains the phenomenon of how his name became attached to the whole corpus of tales:
Once there were no stories in the world. The Sky-God, Nyame, had them all. Anansi went to Nyame and asked how much they would cost to buy.
Nyame set a high price: Anansi must bring back Onini the Python, Osebo the Leopard, the Mmoboro Hornets, and Mmoatia the dwarf.
Anansi set about capturing these. First he went to where Python lived and debated out loud whether Python was really longer than the palm branch or not as his wife Aso says. Python overheard and, when Anansi explained the debate, agreed to lie along the palm branch. Because he cannot easily make himself completely straight a true impression of his actual length is difficult to obtain, so Python agreed to be tied to the branch. When he was completely tied, Anansi took him to Nyame.
To catch the leopard, Anansi dug a deep hole in the ground. When the leopard fell in the hole Anansi offered to help him out with his webs. Once the leopard was out of the hole though he was bound in Anansi’s webs and was carried away.
To catch the hornets, Anansi filled a calabash with water and poured some over a banana leaf he held over his head and some over the nest, calling out that it was raining. He suggested the hornets get into the empty calabash, and when they obliged, he quickly sealed the opening.
To catch the dwarf he made a doll and covered it with sticky gum. He placed the doll under the odum tree where the dwarfs play and put some yam in a bowl in front of it. When the dwarf came and ate the yam she thanked the doll which of course did not reply. Annoyed at its bad manners she struck it, first with one hand then the other. The hands stuck and Anansi captured her.
Anansi handed his captives over to Nyame. Nyame rewarded him with the stories, which now become known as Anansi stories.
(Art by trowica @deviantart)