Taka

Taka, originally Hebi, is the team Sasuke Uchiha created, with the original goal of helping him locate Itachi, and prevent anyone from interrupting his battle. After betraying Orochimaru, Sasuke traveled to various Otogakure bases to recruit his three team-mates, Suigetsu Hōzuki, Karin, and Jūgo. After witnessing Itachi's death, and learning Konoha's role in the Uchiha clan massacre by Madara Uchiha, Sasuke renamed the team "Taka" with the new goal to crush Konoha.

Although their team was originally one of necessity, they all came to respect each other as team-mates and even risked their lives to protect one another as time went on, reminding Sasuke of Team 7. However, as Sasuke became more corrupt and focused in his revenge against Konoha, he abandoned Jūgo and Suigetsu in the Land of Iron to pursue Danzō, and, when Karin became a burden to him, he critically wounded her with the intent to kill her, effectively disbanding Taka.

Motives
Sasuke was initially driven by the desire to avenge his clan by killing his brother, and after learning the truth about his brother, avenging him by destroying Konohagakure. Suigetsu, Karin and Jugo are not exactly fond of one another nor do they really enjoy each other's company. Each of them indicates having their own motive for joining the team upon its formation:
 * Suigetsu: Take ownership of Kisame's Samehada.
 * Karin: Originally claimed to just be going in the same direction, although it was actually her infatuation with Sasuke.
 * Jūgo: Considers Sasuke to be the only successor to Kimimaro, who was the only other person capable of calming his murderous impulse.

Name
The name "Hawk" likely derives from the Japanese proverb. It normally means that an extraordinarily gifted child can be born from ordinary parents. However, here it gains an extra meaning, since Tobi (whose name means kite) was responsible for the reformation of Hebi into Taka.

Trivia

 * Three of the group members' eye color matches with their hair color: Sasuke Uchiha (black), Karin (red) and Jūgo (orange).
 * And the fourth member, Suigetsu Hōzuki, while not having eyes that match his hair, has an eye color that matches the shirt he commonly wears (purple).
 * All of the members of Taka, when recruited by Sasuke, had an additional side story that only appeared in the anime. Through these, their abilities were shown earlier than in the manga.
 * Suigetsu had to retrieve his sword from Tenzen Daikoku. His Hydration Technique was shown.
 * Karin had a flashback of her helping Sasuke retrieve a group of escaped prisoners. Her Mind's Eye of the Kagura technique was shown.
 * Jūgo had a flashback of being recruited by Kimimaro to join Orochimaru. His Cursed Seal ability was briefly shown.