That error message is being displayed by the VB6 program. You can have the code ignore the message and do something else instead of just displaying the generic Jet message.

You need to find the event procedure where this error message is being displayed. You say "if a user enters a duplicate Label", which is a little vague. The user probably has to click a command button to add the new label, so open that command button's click event by double clicking the command button in design view. There is probably an error handler in that event procedure along the lines of:
Code:
Private Sub cmdAdd_Click()
On Error Goto cmdAddErr

    [some code here to add the new label]

cmdAddExit:
    Exit Sub

cmdAddErr:
    MsgBox Err.Description
    Resume cmdAddExit
End Sub
The key is to find the MsgBox command in the error handler. Change that MsgBox line to this:

MsgBox Err.Description, vbInformation, Err.Number

Then purposely add a duplicate label. Then look at the msgbox and you'll see the error number in the blue caption bar instead of "MicroStation." Armed with the error number, change the error handler to:
Code:
cmdAddErr:
    If Err.Number = # Then
        ' We have a duplicate; do something here
    Else
        MsgBox Err.Description
    End If
    Resume cmdAddExit
End Sub
Where you plug the actual error number in place of the pound (#) sign. Once you've gotten this far, you'll at least know where to make your change. You'll probably need to post back here with several more questions before we can this issue totally squared away. Not a problem; we can help you. A good first step would be to post the contents of the commend button's event procedure here so we can see what you're dealing with.