<fieldset>
        <legend>Значок веб-страницы</legend>
        <input name="icon" type="radio" value="no_icon" checked> Не устанавливать
        <input name="icon" type="radio" value="yes_icon"> Установить
    </fieldset>
    <div style="height: 0px"></div>
   
    <fieldset>
        <legend>Заголовок веб-страницы</legend>
        <input name="title" type="radio" value="no_title" checked> Не устанавливать
        <input name="title" type="radio" value="yes_title"> Установить
    </fieldset>
    <script>
        const delay = ms => new Promise(resolve => { setTimeout(resolve, ms); });
 
        for (let radio of document.querySelectorAll("fieldset [type='radio']"))
            radio.onchange = radio_change;
 
        async function radio_change() {
            await delay(0);
            alert(this.value);
        }
    </script>

<div id="radio1" class="radio1">
    <template v-for="(val, id) in values">
        <input type="radio" :id="id" v-model="selectedValue" :value="val.value">
        <label :for="id">{{val.name}}</label><br>
    </template>    
    <p v-if="selectedValue!==null">{{selectedValue}}={{name}}</p>
<script>var radio1 = new Vue({el: '#radio1',
        data: {values:[{name:'Не устанавливать', value: 1}, {name:'Устанавливать', value: 2}], selectedValue: 1}});</script>
</div>
<div id="radio2" class="radio2">
    <template v-for="(val, id) in values">
        <input type="radio" :id="id" v-model="selectedValue" :value="val.value">
        <label :for="id">{{val.name}}</label><br>
    </template>    
    <p v-if="selectedValue!==null">{{selectedValue}}={{name}}</p>
<script>var radio2 = new Vue({el: '#radio2',
        data: {values:[{name:'Не устанавливать2', value: 1}, {name:'Устанавливать2', value: 2}], selectedValue: 1}});</script>
</div>

<div id="radio11">
    <input type="radio" value="Tom11" v-model="user"><label>Tom11</label><br>
    <input type="radio" value="Bob11" v-model="user"><label>Bob11</label><br>
    <span>Выбрано: {{ user }}</span>
<script>var radio11 = new Vue({el: '#radio11', data: {user:''}});</script>
</div>

<script>var radio11 = new Vue({el: "#radio11", data: {user:""}});</script>
<script>const radio11 = new Vue({ el: "#radio11", data: { user: "Bob11" } });</script>

<div id="radio11">
    <input type="radio" value="Tom11" v-model="user"><label>Tom11</label><br>
    <input type="radio" value="Bob11" v-model="user"><label>Bob11</label><br>
    <span>Выбрано: {{ user }}</span>
    <script>const radio11 = new Vue({el: "#radio11", data: {user: "Bob11"}});</script><!--установит выбранной радиокнопку-->
</div>

<div id="radio22">
    <input type="radio" value="Tom22" v-model="user"><label>Tom22</label><br>
    <input type="radio" value="Bob22" v-model="user"><label>Bob22</label><br>
    <span>Выбрано: {{ user }}</span>
<script>const radio22 = new Vue({el: "#radio22", data: {user: ""}});</script><!--НЕ установит выбранной радиокнопку-->
</div>

//скрипт JavaScript - НЕ Vue!! 
	for (let radio of document.getElementsByName("header")) radio.onchange = radio_change;
    function radio_change() {alert(this.value);}

//скрипт JavaScript - НЕ Vue!! 
	for (let radio of document.getElementsByName("header")) radio.onchange = radio_change;
    function radio_change() {alert(this.value);}

//скрипт JavaScript - НЕ Vue!! 
	for (let radio of document.getElementsByName("header")) radio.onchange = radio_change;
    function radio_change() if this.value="Не устанавливать" {alert(this.value);}