All perfect praise be to Allah
Firstly, as we all know this topic of magic etc is huge, and definitely not for everyone to dig deep in. Because it is complex and can lead some people to get involved in magic willingly or unwillingly. So, i will try to be as short as possible, and will not advice anyone to dig deep in this, until or unless they have strong relation with Allah, have strong routines of masnoon prayers etc, because this acts like a protecter for you from being astray.
Now, coming to the question. You basically asked about if this is black magic, and how it works. And what are its effects.
Is it black magic and how this works?
Who knows! can be black magic can be any other form of magic or someone just wrote names because he saw someone writing same, and thought this will be magical...
It's not the mere words which matter, it is the whole process of how these words got written, who and why and how wrote these words.
Magic is not just writing a few words, it is a whole satanic process of making contact with shayateen, than making them happy by doing whatever they want you to do, sacrificing on their names instead of Allah's and doing all kind of crazy disgusting and haram stuff(I really can't explain how disgusting these can be, just as an example, women's period blood might be used to write/drink or whatever shaitaan wants him to do with it...). Basically to make shaitaan happy, and then shaitaan ensures magician that he will assist him in his matter if he writes this and that for someone and say these words or do something for it before giving it to the person who need it.
How shaitaan assist in it? that a whole long topic.(jinns are usually used in the process)
Is there any harm destroying it?
There can be! And if it's real black magic than tis more likely to harm you if you are weak in your iman or aamaal or both, and if you are weak in your regular routine prayer+zikr. That's exactly why you should avoid doing it and give it you any person you think is better in aamaal and iman than you and he knows how to deal with this stuff. There are general instructions too, which if followed will inshallah ensure you are not harmed, these instruction just include some masnoon zikr like ayat-al-kursi darood some other quranic verses etc.
In short, you should avoid messing with magic if you don't know what you are doing. For your own safety. Some magical taweez also have some kind of powder in it, which is another kind of magic and this kind is more likely to harm anyone who opens or tries to destroy this without any precautions.
I would suggest this FB page which aims to help and urge people destroy their taweez, i remember they had an informative how to on destroying taweez too, which is very good. Jazakallah for them.
I hope this answers your question.
Allah knows best