When we enter a nickname in demographic info, is that viewable by the parents when they log into their Powerschool account?
Is it viewable on the student's account when they log in to their own account?
Is the field referred as "Nickname"? If so, that may be a customization. PowerSchool by default has the name fields in Demographics and then Legal Names (If different) on the registration page. Unless you have an additional customization showing the nickname in the public portal / app - the answer here is probably "No".
Edit: corrected registration page information
Yes, it is labeled 'nickname'
That is almost certainly a page customization then. Without more information, it would be hard to say for certain that it won't be mirrored on the public portal side. You may want to find a helpful parent and test it.