index.js

import Vue from 'vue';
import Vuex from 'vuex';
import * as actions from './actions';
import * as getters from './getters';
import user from './modules/user/user';

Vue.use(Vuex);

const debug = process.env.NODE_ENV !== 'production';

export default new Vuex.Store({
  actions,
  getters,
  modules: {
    user,
  },
  strict: debug,
});

Login.vue

....
created: () => console.log(mapState('user', ['username'])), //for debug
computed: {
  ...mapState('user', ['username'])
},
....

user.js

import * as mutationTypes from './mutation_types';
import * as actionTypes from './action_types';

const state = {
  username: '',
  pending: false,
};

const getters = {
  isLoggedIn: () => !(localStorage.getItem('token') === null),
};

const actions = {
  [actionTypes.LOGIN]({ commit }, credentials) {
    commit(mutationTypes.LOGIN_START); // show spinner
    return new Promise((resolve) => {
      setTimeout(() => {
        const result = true;
        if (result) {
          /* eslint no-console: [0] */
          const credentialsString = ' '.concat(...credentials);
          console.log(`Logging with credentials ${credentialsString}`);
          localStorage.setItem('token', 'JWT');
          commit(mutationTypes.LOGIN_SUCCESS, credentials);
          resolve();
        } else {
          commit(mutationTypes.LOGIN_FAILED, credentials);
          resolve();
        }
      }, 1000);
    });
  },
  [actionTypes.LOGOUT]({ commit }) {
    localStorage.removeItem('token');
    commit(mutationTypes.LOGOUT);
  },
};

/* eslint no-shadow: ["error", { "allow": ["state"] }] */
const mutations = {
  [mutationTypes.LOGIN_START](state) {
    state.pending = true;
  },
  [mutationTypes.LOGIN_SUCCESS](state, credentials) {
    state.pending = false;
    state.username = credentials.username;
  },
  [mutationTypes.LOGIN_FAILED](state) {
    state.pending = false;
  },
  [mutationTypes.LOGOUT](state) {
    state.isLoggedIn = false;
  },
};

export default {
  namespaced: true,
  state,
  getters,
  actions,
  mutations,
};