How to get the text of the selected option using vuejs?

Instead of define the value only as the id, you can bind the selected value with an object with two attributes: value and text.
For example with products:

<div id="app">
   <select v-model="selected">
       <option v-for="product in products" v-bind:value="{ id: product.id, text: product.name }">
         {{ product.name }}
       </option>
   </select>
</div>

Then you can access to the text through the “value”:

   <h1>Value:
     {{selected.id}}
   </h1>
   <h1>Text:
     {{selected.text}}
   </h1>

Working example

var app = new Vue({
  el: '#app',
  data: {
  	selected: '',
    products: [
      {id: 1, name: 'A'},
      {id: 2, name: 'B'},
      {id: 3, name: 'C'}
    ]
  }
})

<div id="app">
   <select v-model="selected">
       <option v-for="product in products" v-bind:value="{ id: product.id, text: product.name }">{{ product.name }}
       </option>
   </select>
   <h1>Value:
   {{selected.id}}
   </h1>
   <h1>Text:
   {{selected.text}}
   </h1>
</div>
<script src="https://unpkg.com/vue@2.4.4/dist/vue.js"></script>