Assuming the link to the document is a separate paragraph (and the first) in the document, you start with this. If it matches the format you specify, you simply find the last occurrence /, take the name after the found index, and do find-replace to replace all the occurrences ~Name~.
Sub ReplaceNames()
Dim ref As String
ref = ActiveDocument.Paragraphs(1).Range.Text
Dim name As String
name = Mid(ref, InStrRev(ref, "/") + 1)
'If name ends with a paragraph, remove it.
If Right(name, 1) = Chr(13) Then name = Left(name, Len(name) - 1)
ActiveDocument.Range.Find.Execute "~Name~", MatchCase:=False, ReplaceWith:=name, Replace:=wdReplaceAll
End Sub
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