[quote user="Jon Summers"]
Take a look at VBA's Like operator.
[/quote]
Thanks that helps some. In my case it wasn't learning how to use the wildcard so much as it was learning where to put the "Not" operator. This alteration seems to work the same and the wildcard makes it a little less code to pick the file or files I want to exclude.
Sub SetLogNameAsDefLogName()
Dim att As Attachment
For Each att In ActiveModelReference.Attachments
If Not att.AttachName Like "*Profile*" Then
On Error Resume Next
att.LogicalName = att.DefaultLogicalName
att.Rewrite
End If
Next
End Sub