Except if there is the possibility of it happening without their knowledge/consent, the other person could use even the name for further social engineering. It’s better to not give out any information automatically. Granted the user has to approve a Name Drop share but the screen does display the user’s contact info that would be shared either way, so if the phone is visible to the person trying to obtain the info, they’d still be able to see it even if the target doesn’t approve the share.
It is a bit overhyped since it’s not like someone shady can go around sniffing everyone’s contacts automatically, but it’s still worth tuning off for anyone who is privacy or security conscious.
If that is the case then it’s better but I’d still shut it off and err on the side of caution. The Apple demo video does not mention needing Air Drop enabled, only that both users need to be signed into iCloud: https://www.youtube.com/watch?v=aZL5D1k-4aI