Simpler:
Code:
Sub Demo()
Dim Tbl As Table
For Each Tbl In ActiveDocument.Tables
With Tbl
.Range.Bookmarks.Add Split(.Cell(1, 1).Range.Text, vbCr)(0), .Range
End With
Next Tbl
End Sub
As with Greg's code, though, if the content of the first paragraph in the first cell isn't valid for a bookmark, you'll get an error.