You need to call Vue.set() for arrays, and NOT use indexing such as

foo[3]= 'bar'

Vue DOES recognize some operations, such as splice and push, however.

Read more about it here: https://vuejs.org/2016/02/06/common-gotchas/ and here: https://v2.vuejs.org/v2/guide/list.html#Array-Change-Detection

So for your code, and using the Vue handy helper method $set:

this.validated.$set(name, true);

Why…

Javascript does not offer a hook (overload) for the array index operator ([]), so Vue has no way of intercepting it. This is a limitation of Javascript, not Vue. Here’s more on that: How would you overload the [] operator in javascript