Get all name values from html option tag in javascript

Assuming that ES6 is an option for you, then the following will do as you wish:

// using a named function:
function grabTextFrom() {

  // initialising the local variable using 'let',
  // converting the argument supplied to Array.from()
  // to convert the Array-like Object (in this case
  // a NodeList, or HTMLCollection, from
  // document.querySelectorAll()) into an Array:
  let texts = Array.from(
    document.querySelectorAll(

      // 'this' is passed automatically from the
      // later use of EventTarget.addEventListener(),
      // and the dataset.textFrom property value is
      // the value stored in the data-textfrom attribute:
      this.dataset.textfrom
    )

  // iterating over that Array of elements using
  // Array.prototype.map() along with an arrow function:
  ).map(

    // 'opt' is a reference to the current Array-element
    // from the Array of elements over which we're iterating;
    // and here we return the value property-value of that
    // current element:
    opt => opt.value
  );

  // logging to the console for demo purposes:
  console.log(texts);

  // returning to the calling context:
  return texts;
}

// finding the first element which matches the
// supplied CSS selector, and adding the
// grabTextFrom() function as the event-handler
// for the 'click' event (note the deliberate
// lack of parentheses in the function-name):
document.querySelector('#submit').addEventListener('click', grabTextFrom);

function grabTextFrom() {
  let texts = Array.from(
    document.querySelectorAll(this.dataset.textfrom)
  ).map(
    opt => opt.value
  );
  console.log(texts);
  return texts;
}

document.querySelector('#submit').addEventListener('click', grabTextFrom);

<select id="options">
  <option>Joe</option>
  <option>Buckey</option>
  <option>Elen</option>
  <option>Rimzy</option>
</select>
<button id="submit" data-textfrom="option">Submit</button>

If, however, you have to provide for ES5 compatibility then the following will work identically:

function grabTextFrom() {

  // here we use Array.prototype.slice(), along
  // with Function.prototype.call(), to apply
  // the slice() method to the supplied NodeList:
  var texts = Array.prototype.slice.call(
    document.querySelectorAll(this.dataset.textfrom)

  // here we use the anonymous function of the
  // Array.prototype.map() method to perform the
  // same function as above, returning the
  // opt.value property-value to the created Array:
  ).map(function(opt) {
    return opt.value;
  });
  console.log(texts);
  return texts;
}

document.querySelector('#submit').addEventListener('click', grabTextFrom);

function grabTextFrom() {
  var texts = Array.prototype.slice.call(
    document.querySelectorAll(this.dataset.textfrom)
  ).map(function(opt) {
    return opt.value;
  });
  console.log(texts);
  return texts;
}

document.querySelector('#submit').addEventListener('click', grabTextFrom);

<select id="options">
  <option>Joe</option>
  <option>Buckey</option>
  <option>Elen</option>
  <option>Rimzy</option>
</select>
<button id="submit" data-textfrom="option">Submit</button>