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this is because each child component creates separate v-radio-group. if you create a separate component for v-radio-group and use it as a wrapper on your child component then it should work.
example.
MyRadioGroup.vue
<template>
<v-radio-group> <!--also props for these if required-->
</v-radio-group>
</template>
MyRadio.vue
<template>
<v-radio :name="name" :value="value" @change="inputChange" />
</template>
Now you can use these as below
<MyRadioGroup>
<MyRadio></MyRadio>
<MyRadio></MyRadio>
<MyRadio></MyRadio>
</MyRadioGroup>
Source:stackexchange.com