Assign contact to a new Owner.

Assign.cs

contact.FirstName = "Tom";

// Assign record to new owner
AssignRequest assign = new AssignRequest
{
    Assignee = new EntityReference(SystemUser.EntityLogicalName, newOwnerId),
    Target = new EntityReference(Contact.EntityLogicalName, contact.Id)
};

_context.UpdateObject(contact);

_context.Execute(assign);

_context.SaveChanges();