v-if and v-else inside of v-for for different text rendering

Use another template element like following (not tested)

<template>
    <ul v-show="showNotifications">
        <li v-for="notification in notifications">
            <template v-if="notification.type == 'friend request'">
            New friend request from {{ notification.name }}
            </template>
            <template v-else>
            New notification from {{ notification.name }}
            </template>
       </li>
   </ul>