[Vuejs]-What is the best practice for reactive setter for an object in array in Vuex?

With vuex, you want to be using actions and mutations.

setLanguage: (e, index) => {
  let name = e.target.value.trim()
  this.$store.dispatch('setLanguage', {name, index}) //dispatches a vuex action
}

Then define an action:

setLanguage({ commit }, payload) {
  commit('setLanguage', payload) //commits a vuex mutation
}

And finally a mutation:

setLanguage(state, payload) {
  state.languages[payload.index].name = payload.name
}

see the vuex documentation on this: https://vuex.vuejs.org/guide/actions.html