index3.html

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Document</title>
    <!-- development version, includes helpful console warnings -->
    <script src="https://cdn.jsdelivr.net/npm/vue/dist/vue.js"></script>
</head>
<body>
    <div id="app">
        
        <input type="text" v-model="name" />

        <input type="text" id="surname" value="Snow"  />
        <button @click="saveSurname"> Save Surname </button><br/><br/>
        <output>{{computedFullName}}</output>
    </div>

</body>
<script>
        let surname = "Snow";
    var app= new Vue({
        el:'#app',
        data:{
            name:'John',
        },
        computed:{
            computedFullName: function(){
                return this.name + ' ' + surname;
            }
        },
        methods:{
            saveSurname: function(){
                surname = this.$el.querySelector('#surname').value;
            }
        }
    });

</script>