Kenpachi Zaraki
Note: The only Captain who didn’t take the exam to become a Shinigami.
Zaraki’s surname comes from the district he once resided in, Zaraki, which is district #80 of the North Alley of Rukongai. District #80 is the worst, most lawless region of Rukongai, full of thieves and murderers (whereas area #1 is the most orderly and law-abiding). While residing in District #80, Kenpachi was nameless. During that time, he became proficient in swordsmanship and killed numerous enemies.
At some point during his travels outside of District #80, he found a small girl and named her Yachiru (八千流), in remembrance of the only person he ever admired, after she showed no fear of his sword. Yachiru came from area #79, Kusajishi (草鹿), where her parents were murdered. The two events were apparently quite close. On that day, he also took on a name: Kenpachi, the title bestowed upon the strongest swordsman, the one who has killed the most. The two developed a father-daughter-like relationship.
Also, at some point (before he became a Captain), he fought and defeated Ikkaku Madarame; for this reason, Ikkaku pledged to serve under Kenpachi from there on out (Ikkaku doesn’t actually get the chance to do so until he joins the 11th Division), but Ikkaku would still jump at the chance to fight Kenpachi to the death.
After some time had passed, Kenpachi found his way to the Seireitei. He defeated and killed the previous Captain of the 11th Division (whose identity is currently unknown) and gained his seat in the Gotei 13 in this manner. In the anime, his assumption of the Captain’s seat caused Maki Ichinose to leave the Soul Society. According to the anime, it is also what convinced Ikkaku and Yumichika to join the Shinigami.