You could probably use MimeData.GetHashCode for that.
[Edit]
From Mail.dll's perspective, if you are recreating MaimeData object, this is a new object - there is no need for it to store some kind of id internally.
It is your scenario that, makes this object somehow equal to the previous one. Please note, that the problem you are facing is not at all Mail.dll related.
Consider computing hash from the raw data, if you believe same file name is not enough.