пихаем это в Книгу

Private Sub Workbook_Open()
        'ведение лога
        UserLog
End Sub

непосредственно код в модуле

Private Declare Function GetComputerNameA Lib "kernel32" (ByVal lpBuffer As String, nSize As Long) As Long
Private Declare Function WNetGetUserA Lib "mpr.dll" (ByVal lpName As String, ByVal lpUserName As String, lpnLength As Long) As Long
'сетевое имя компьютера
Function GetComputerName() As String
Dim sBuffer As String * 255
If GetComputerNameA(sBuffer, 255&) <> 0 Then
GetComputerName = Left$(sBuffer, InStr(sBuffer, vbNullChar) - 1)
End If
End Function
'имя пользователя
Function GetUserName() As String
Dim sUserNameBuff As String * 255
sUserNameBuff = Space(255)
Call WNetGetUserA(vbNullString, sUserNameBuff, 255&)
GetUserName = Left$(sUserNameBuff, InStr(sUserNameBuff, vbNullChar) - 1)
End Function
'запись в лог-файл
Sub UserLog()
Dim nLogtxt As String

nLogtxt = "G:\PROJECTS\LogData" & "\" & Replace(ThisWorkbook.Name, ".xls", ".txt")

        Open nLogtxt For Append As #1
            Print #1, Application.UserName & " -- " & Now & " -- " & GetComputerName & " -- " & GetUserName
        Close #1
End Sub