There are plenty of strata schemes that don’t “name and shame” levies defaulters, based on the simple logic that they have enough problems without becoming social pariahs too. Usually this is extended to owners who have made an effort to explain why they are behind with their levies and what they plan to do about it.
As for owners who don’t give a stuff about what effect their slow payment has on their neighbours, I would make sure their names were out there and why.
The strata committee can instruct the strata manager on how they want information to be revealed but you can’t stop owners accessing information that they have a right to know.