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 teammates, Suigetsu Hōzuki, Karin, and Jūgo. After killing Itachi, 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 came to consider each other teammates and risked their lives to protect each other as time went on. 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 critically wounded with the intent to kill Karin when she became a burden to him.

Motives
In addition to Sasuke's goals of avenging the Uchiha clan (initially by killing Itachi Uchiha, then by destroying Konohagakure), each member 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), but as she has loyally stayed with the team through everything since her recruitment, it seems that this explanation no longer holds much water.
 * Jūgo: Considers Sasuke to be the only successor to Kimimaro, who was the only other person capable of calming his murderous intent.

Additionally, although they were somewhat indifferent to each other at first, they came to consider each other teammates and risked their lives to protect each other as time went on. 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 Karin was critically wounded and abandoned by Sasuke himself once she became a burden to him.

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 members of Taka have matching eye and hair colors: Sasuke Uchiha (black), Karin (red) and Jūgo (orange).
 * And the fourth member, Suigetsu Hozuki, 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.