I want to make a business page but not related to my Facebook profile so if I make a profile with no real human name, will I have a problem? Is Facebook going to delete it?
Ideally, when you create a Facebook page, it is not publicly known as to who actually created that page. You can actually post, like and even share as a page vs an individual. In that case, you need not need another profile to create a Facebook page.
Having said all this, you need not have an issue using a fake name. Actually, a ton of people in the SEO world make and delete fake profiles all the time (I know a few people who do it too for various "other" reasons)
Let me know if you need more help!