The Hyuuga/Uzumaki Company is an alliance formed between the Hyuuga Company and the Uzumaki Company.
The formation of the alliance came due to the fact the Hyuuga Company was having a crisis, and, as so, the Uzumaki Company leader Minato Namikaze decided to help the rival company by forming an alliance. The deal was accepted, however, in the night when the deal was to be fulfilled, someone sabotaged it, and the incident ended with the death of both Minato Namikaze and Hiazashi Hyuuga.
Minato Namikaze was the previous leader of the Uzumaki Company, how he got the position is unknown, since he doesn't belong to the Uzumaki family. However, it's possible he it through the marriage he had with Kushina Uzumaki, who did belong to the family.
Jiraiya took over the Uzumaki Company after Minato's death, since he is Naruto's tutor and the boy was too young to run a company.
Hiashi was the leader of the Hyuuga Company up until the formation of the alliance. His brother Hizashi seemed to have an important position in the Company, considering the he attended to the first agreement.
It is yet to be seen who the leader or the heir of the Alliance is, since little time has passed since its formation. It is possible its heir is Naruto Uzumaki, because of his relationship with Hinata, however, there is no evidence of it.