Call build on Text widget when i change tab

Inside the TabBar widget, add onTap callback with the setState method to trigger rebuild, hence updating the name:

...
appBar: AppBar(
  title: Text(tasksListLabels[_tabController.index].longName),
  bottom: TabBar(
    controller: _tabController,
    isScrollable: true,
    tabs: [
      Tab(text: tasksListLabels[0].shortName),
      Tab(text: tasksListLabels[1].shortName),
      Tab(text: tasksListLabels[2].shortName),
      Tab(text: tasksListLabels[3].shortName),
      Tab(text: tasksListLabels[4].shortName),
      Tab(text: tasksListLabels[5].shortName),
    ],
    onTap: (_) {
      setState((){});
    },
  ),
),
...