You can use lodash#map to transform each item in the user array and lodash#mapKeys to transorm each of the user item's keys.
const result = _.map(user, data => 
  _.mapKeys(data, (v, k) => k.replace(/^y_/, '')));
const user = [
  {"data":"2","y_data1":1},
  {"data":"4","y_data1":3,"y_data2":3}
];
const result = _.map(user, data => 
  _.mapKeys(data, (v, k) => k.replace(/^y_/, '')));
console.log(result);
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<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.10/lodash.min.js"></script>
 
 
Pure JS solution: Use Array#map for the item transformation, and a combination of Object.entries() and Array#reduce to achieve the key transformation.
const result = user.map(data =>
  Object.entries(data).reduce(
    (r, [k, v]) => (r[k.replace(/^y_/, '')] = v, r),
    {}
  )
);
const user = [
  {"data":"2","y_data1":1},
  {"data":"4","y_data1":3,"y_data2":3}
];
const result = user.map(data =>
  Object.entries(data).reduce(
    (r, [k, v]) => (r[k.replace(/^y_/, '')] = v, r),
    {}
  )
);
console.log(result);
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