<ComboBox ItemsSource="{Binding CustomerTypes}" DisplayMemberPath="Name"  
                          SelectedItem="{Binding Path=CurrentCustomerType}" 
                          SelectedValue="{Binding Path=CurrentCustomerType.Id}"
                          SelectedValuePath="Id"
                          IsSynchronizedWithCurrentItem="True"/>

public CustomerCardViewModel()
        {
            _clientLayer = new ClientLayer();
            CurrentCustomer = new Customer();
            _customerTypes = new ObservableCollection<CustomerType>(_clientLayer.GetAllCustomerTypes());
         }

        public Customer CurrentCustomer
        {
            get { return _currentCustomer; }
            set { SetProperty(ref _currentCustomer, value); }
        }

        public CustomerType CurrentCustomerType
        {
            get { return _currentCustomerType; }
            set 
            {
                if (_currentCustomer.CustomerType != value) 
                {
                    _currentCustomer.CustomerType = value;
                    _currentCustomer.CustomerTypeId = value.Id;
                }
                SetProperty(ref _currentCustomerType, value); 

            }
        }

        public ObservableCollection<CustomerType> CustomerTypes
        {
            get { return _customerTypes; }
         }