The log book is a personal document, how you fill it in and what you put in it is up to the holder. In the UK the ANO Article 228 details what you must legally record, so long as you have met that requirement you can do whatever else you like.
If you are PIS the Examiner is PIC. You log your operating capacity as PIS or PICUS which requires the Examiner to endorse it.
CAP 804 Section 1 Part E Para 9
