This assumes you're asking about the past and not the future use of the workbook. AFAIK, the best you'll be able to do is see who modified it last (Info in backstage - opened by File menu & Info from list). If you opened and saved it before you noticed it was changed, then the modifier will be you.
If you're asking about future use and don't want to turn on tracking then I believe you'll have to use code and store the name somewhere - perhaps a hidden sheet or just a hidden column on a sheet.
Option Explicit
PrivateSub Workbook_Open()Dim LR AsLongWith Sheets("Sheet1")
LR =.Range("A"& Rows.Count).End(xlUp).Row
.Range("A"& LR +1).Value = Time
.Range("B"& LR +1).Value = Environ("UserName")
ThisWorkbook.Save
EndWithEndSub
You can change the Sheet name to something else and hide that sheet from the user's view.
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