[SuperZen]

const users = [
  {
    name: 'Dima',
    age: 39,
    phone: '099-245-45-45'
  },
  {
    name: 'Vasya',
    age: 28,
    phone: '066-500-49-45'
  },
  {
    name: 'Kolya',
    age: 39,
    phone: '063-100-20-13'
  }
];

let userKey = 'Dima';
getUserData(userKey, users);

function getUserData(userKey, userArray) {
  for (let i = 0; i < userArray.length; i++) {
    if ((userArray[i].name == userKey) || (userArray[i].phone == userKey)) {
      console.log('Имя пользователя: ' + userArray[i].name);
      console.log('Возраст пользователя: ' + userArray[i].age);
      console.log('Телефон пользователя: ' + userArray[i].phone);
      return userArray[i]
    } 
  }
  console.log('Пользователь в БД не найден');
}

или тоже самое:

const users = [
  {
    name: 'Dima',
    age: 39,
    phone: '099-245-45-45'
  },
  {
    name: 'Vasya',
    age: 28,
    phone: '066-500-49-45'
  },
  {
    name: 'Kolya',
    age: 39,
    phone: '063-100-20-13'
  }
];

const getUserData = key => users.find(u => u.name.toLocaleLowerCase() === key.toLocaleLowerCase() || u.phone === key) //  dima === DiMa
// null = not found
console.log(getUserData('dima'))