You can lock down your profile so tightly that no one can find you - make sure you only have the minimum information posted that is necessary to run the account, and have that set to 'private'. The only thing that MusT be public is your name & profile pic, but you can choose to leave the pic blank or use a generic photo of a flower etc. If you're worried about being tracked by an unusual name, I'd either use a nickname or middle name instead - or a misspelling. I have a friend who has put a deliberate typo in her name and reversed her first and surname. So, for example, Charlotte Smith becomes Smyth Charelott.
You can set your preferences so that no one can send you a friend request. You can also make yourself 'unsearchable' by your email/phone number. And if you want to make sure your profile is private enough, you can click on the three dots on the header and click on 'view as' public. This shows what your profile looks like to a random browser - I check this regularly, to ensure I haven't accidently made something public without realising it.
I have to have a FB account as I run a group page, but I'm very careful who can see it and what information I post on it!