Would really need to see the context in which it is used.
The party named in this document...
This would mean the individual named or group named in the document. At some point in the document there is a company name or an individuals name and the party named is refering to that company or individual.
Client means the party named in the Contract, who employs the Consultant, and legal successors to the Client and permitted assignees = Cliente significa la parte nombrada en el Contrato, la cual emplea al Consultor y los sucesores legales del Cliente y cesionarios permitidos.