If you want the employee name to get displayed based on id, the simplest way is just pass that id to a function and return the name, like as shown below

Working Demo

html

<div ng-app='myApp' ng-controller=ArrayController>

    <li ng-repeat=employment in Employments>{{getEmployeeName(employment.user_id)}}

    </li>

</div>

script

var app = angular.module('myApp', []);

app.controller('ArrayController', function ($scope) {

    $scope.Users = [{

        id: 1,

        name: ryan

    }, {

        id: 2,

        name: Julie

    }];



    $scope.Employments = [{

        user_id: 1,

        title: manager

    }, {

        user_id: 2,

        title: Professor

    }];



    $scope.getEmployeeName = function (empId) {

        for (var i = 0; i < $scope.Users.length; i++) {

            if ($scope.Users[i].id === empId) {

                return $scope.Users[i].name;

            }

        };

    };

});

UPDATE 2

If you want to embed the User array in the Employments array, try the following stuff

$scope.Users = [{id: 1, name: ryan}, {id: 2, name: Julie}];



$scope.Employments = [{user_id: 1, title: manager}, 

                      {user_id: 2, title: Professor}

                     ];

code for flattening Employments array by adding User properties

angular.forEach($scope.Users, function (user, userIndex) {

    angular.forEach($scope.Employments, function (employee, employeeIndex) {

        if (employee.user_id === user.id) {

            employee.name = user.name;

        }

    });

});

Output

$scope.Employments = [ { user_id: 1, title: manager, name: ryan }, 

                       { user_id: 2, title: Professor, name: Julie } 

                     ]

Working Demo

UPDATE 3

Code for making a nested employee structure like as shown below from $scope.Users and $scope.Employments

$scope.employees = [];

angular.forEach($scope.Employments, function (employee, employeeIndex) {

    var employeeObject = {};

    employeeObject.title = employee.title;

    angular.forEach($scope.Users, function (user, userIndex) {

        if (employee.user_id === user.id) {

            employeeObject.user = user;

        }

    });

    $scope.employees.push(employeeObject);

});

Output

[ { title: manager, user: { id: 1, name: ryan } }, 

  { title: Professor, user: { id: 2, name: Julie } } 

]

Working Demo