Tsuzuki has had quite a history of partners during his 70+ year term in the Shokan division. Although we, the readers, are not privy to the identity of these massive amounts of individuals, we are allowed the knowledge of four of those individuals, one of which we don't know the name of.
In chronological order of how they are presented in the story, we are first greeted with the dissolvement of Tsuzuki's latest partnership. We don't know much about this man; his personality, his history, or the details of his and Tsuzuki's partnership. The only thing we know for certain is his apparent ecstatic delight in being released from the partnership. All of which takes place in the opening of the series.
Tsuzuki's replacement partner is known as Asuka.... He is a short-term partner with him for only the duration of one case.
Hisoka, a new, young shinigami who dies at 16. He is quite similar in appearance to Asuka.