No, Taekook is not an official couple. The term "Taekook" is a fan-created portmanteau combining the names of BTS members Taehyung (V) and Jungkook. It represents the perceived romantic relationship between these two members, which is an interpretation and creation of fans. BTS and their management, Big Hit Music, have never confirmed or officially recognized Taekook as an actual romantic pairing.
In short, the relationship exists primarily within the realm of fan fiction, speculation, and "shipping" culture.
