The knives that pop out with the press of a button or a flick of the wrist are commonly referred to as "automatic knives," "switchblade knives," or simply "switchblades."
Switchblade knives have a spring-loaded mechanism that allows the blade to be rapidly deployed with one hand. They are designed for quick and easy opening, making them convenient for various tasks. However, it's essential to note that the legality of owning or carrying switchblade knives varies by region. In some places, they may be restricted or prohibited, while in others, they might be allowed under specific regulations. Always check your local laws and regulations regarding knife ownership and carry to ensure you are in compliance.