A double-edged katana is often referred to as a "Ken" or "Ken-style" sword. The term "ken" is derived from the Japanese word for sword. While the term "katana" typically refers to a single-edged curved sword with a sharp cutting edge on one side, the term "ken" encompasses double-edged swords.

It's important to note that the term "ken" can be used broadly to refer to various types of double-edged swords in Japanese history, including straight-bladed swords like the tachi or uchigatana. The specific naming and categorization of swords can vary depending on the historical period, region, or context in which they were used.

In general, the term "ken" is used to distinguish double-edged swords from the single-edged curved blades typically associated with the term "katana."