I'm not sure my understanding of a "trip report" is the same as yours.
In my understanding it is the record of an employee's off-site movement on behalf of the organization (for any specific purpose.)
Depending upon the number of reports and the number of different individuals involved, some sort of organization seems to be necessary. For a few per year, they might have no identification other than content and date of trip, then be filed in a single folder in chronological order, regardless of identity of person making the trip. More reports and more individuals might mean separate sub folders for each trip taker, also in chronological order.
If by "ID number" you are referring to the blank form used by the trip taker to record information and data, I can categorically say there is no requirement to assign an ID number to any document or form. The original purpose for organizations to assign numbers to documents was for ease of storage and retrieval of hard copies. This was necessary ONLY when there were a large number of documents. Otherwise, documents could be stored in folders alphabetically by name or topic.
Modern computer systems make numbering unnecessary because electronic retrieval can find a document wherever it may be stored by searching on key words, dates, authors, etc. Your post indicates you already use this method, so I see no need (need is different from requirement - requirement is mandatory, need is convenience) to add convenience by adding redundant ID numbers.