From Nookipedia, the Animal Crossing wiki
The Walking Stick (ナナフシ, Nanafushi) is a bug that was introduced in Animal Crossing: Wild World. In Animal Crossing: Wild World and Animal Crossing: City Folk, it was called the Walkingstick. They are found from July to November. It is fairly difficult for the player to see it, for at some angles the Walking Stick may blend in with the tree also making its color borders turn gray. When approached they will fade. Starting with Animal Crossing: City Folk, they have a counterpart, which is the Walking Leaf.
Donating to the museum
In City Folk
"Walkingsticks can skillfully disguise themselves as twigs or thin branches. What deceptive wretches! Just imagine going to grab what you thought was a twig and having it go SQUISH in your hand... Such epic foulness! Just thinking about that dark day gives me owl bumps!"
The Walkingstick can be found on the third platform, on the second tree to the left, in the insect exhibition once donated.
In New Leaf
Upon being donated, the Walking Stick can be found in the room of the bug exhibit with the light in, resting on a tree in the back.
"Walking sticks disguise themselves to confuse predators and are very closely related to walking leaves. They have cylindrical bodies that look like sticks. Some of them can even change their pigmentation. Females can lay eggs without the males, so most of the walking sticks you see are females."
Names in other languages