The “census assistant” exists for the purpose of assisting with a transcription of census documents. The purpose of any transcription is to record EXACTLY what was on the original document, so it would be wrong to start debating adding or removing any details. Plus, I’m sure there would never be any agreement.
If you prefer to simply add a shared note of your own preference of details you should just add an ordinary shared note without using the assistant.
Regarding the titles of each column, when you use the assistant the full title is available if you point to the heading of each column both during data entry and on the final display. They are also available on the original document, which of course anyone doing a transcription will have in front of them.