Just add a simple condition e.g.
Public Sub AIG(MItem As Outlook.MailItem)
Dim oAttachment As Outlook.Attachment
Dim sSaveFolder As String
Dim strText As String
    strText = "Text to find"
    sSaveFolder = "C:\Test\"
    For Each oAttachment In MItem.Attachments
        If InStr(1, oAttachment.fileName, strText) > 0 Then
            oAttachment.SaveAsFile sSaveFolder & oAttachment.fileName
        End If
    Next oAttachment
    Set oAttachment = Nothing
End Sub
Note that the path must end in a folder separator character and it is probably better to search the filename than the displayname.