There are essentially two ways to solve it.

Use an existing Package

For example, vue-meta:

<template>
  <div id="app">
    <router-view></router-view>
  </div>
</template>

<script>
  export default {
    name: 'App',
    metaInfo: {
      // if no subcomponents specify a metaInfo.title, this title will be used
      title: 'Default Title',
      // all titles will be injected into this template
      titleTemplate: '%s | My Awesome Webapp'
    }
  }
</script>

Create your own Component

Create a vue file containing:

<script>
    export default {
        name: 'vue-title',
        props: ['title'],
        watch: {
            title: {
                immediate: true,
                handler() {
                    document.title = this.title;
                }
            }
        },
        render () {
        },
    }
</script>

Register the component using

import titleComponent from './title.component.vue';
Vue.component('vue-title', titleComponent);

Then you can use it in your templates, e.g.

<vue-title title="Static Title"></vue-title>
<vue-title :title="dynamic.something + ' - Static'"></vue-title>