Well, turns out answer was simply adding notification to property Courier in Delivery class:

        public Courier? Courier 
    {
        get { return courier; }
        set
        {
            courier = value;
            OnPropertyChanged("NameCourierFull");
        }
    }

That's it, now courier name in DataGrid refresh every time new courier is picked. But funny thing is that if I try to add there OnPropertyChanged("CourierUid") that doesn't help refresh CourierUid. Well I don't need to do it anyway but if anyone knows proper way to make it, I'd still like to know how. Just in case.