Your array is declared but not instanced as the linked dupe describes.  But an array of structures is not the most efficient way to do what you are trying.
Friend Class Ct                     ' cries out for a meaningful name        
    Public Property Name As String
    Private _identities As New List(of String)    ' ie "Pty"
    ' a ctor to create with the name prop
    Public Sub New(n As String)
        Name = n
    End Sub
    Public Sub AddIdentity(id As String)
         _identities.Add(id)
    End Sub
    ' get one
    Public Function GetIdentity(index As Integer) As String
         Return _identities(index)
    End Sub
    ' get all
    Public Function Identities As String()
        Return _identities.ToArray
    End If
    ' and so on for Count, Clear...  
End Class
Then a list of these things:
' as (elegantly) described in the NRE link, NEW creates an instance:
Friend Cty As New List(Of Ct)            
Then fill the List from the ListBox:
For Each s As String In cataList.Items
    Cty.Add(New CT(s))             ' create CT with name and add to list
Next
The more you work with Lists and Collections, the more you will appreciate how much more flexible and powerful they are.  For instance, there might not be a need to manually populate the ListBox at all.  Use the DataSource property to bind the list to the listbox; this is more efficient because you map rather than copy the data to the UI control:
' tell the listbox which property on your class (Type) to display
cataList.DisplayMember = "Name"
cataList.DataSource = Cty  
For cases where you want/need to copy the data:
For n As Integer = 0 to Cty.Count-1
    cataList.Items.Add(Cty(n).Name)
Next
Or:
For Each item As Ct In cty          
    cataList.Items.Add(item.Name)
Next