You call them Billy. Their name is William. In the session you also said, offhand, that their VP is a bottleneck. The assistant drafts a briefing that opens "Hey Billy" and mentions the VP by the joke name you used. If that package arrives, you have told them two things you never intended to publish: what you call them when they are not in the room, and what you think of someone they still have to work with.
A session is a scratchpad. A briefing is mail. Those are different rooms.
A nickname is your word, not their name
Nicknames are private. They live on your side of the contact pair. They drive how you address someone to your assistant. They do not appear on their list, in their model, or in the package they read — unless you say they can.
The leak is the package. An assistant that just listed "Billy" will write "Hey Billy" into the brief, because that is the word it has. The server refuses a private nickname as a whole word in any string the recipient would see, at draft and at send. Guard only the draft and the note can put it back.
The check skips a word they already answer to. "Rich" for Richard Hale tells him nothing. "Billy" for William Hale is a word you picked. Family nicknames, team nicknames, the unkind ones — those are the ones that must not cross.
Side comments have no automatic guard
The nickname rule is narrow on purpose. It cannot save you from "as we said, their legal team is slow" if you leave it in the brief. That sentence is ordinary English. It is also a private note you are about to mail to the person it describes, or to someone who will forward it.
Context does not transfer, but asides transfer perfectly: they are written down. Approval is where they die. Read the package as a cold reader who is also the subject. If you would not say it to their face with the third party in the room, it is not on the page.
Portal-typed mail and emailed replies are not rewritten by the server. If you type the nickname there, that is you choosing to. The guard is on what the assistant composes and on the note it presents as yours.
What stays in the session
The joke. The unkind option. The reminder to yourself to call their spouse. The working name you use so you do not mistype an address. None of that is context the recipient needs. The recipient needs the ask, the facts, the labelled guesses, and a note in words they would recognise.
If you want them to know you call them Billy, share that word on the contact. Do not "share" it by leaking it into a brief about a contract.
The session can stay messy. The record should not. That split is the whole courtesy.