The forum is public, so it is technically searchable. Anyone can look up the forum. However if you don’t give your name or other identifying details, then it would likely be hard for anyone to identify you!
For people that use the forum a lot (mainly reading and liking posts, plus writing a few posts) they get regular status. That means access to a part of the forum called The Lounge which is not public and can only be seen by other regular members. Of course it is still the internet and you are sharing information without any control of what people will do with it. There isn’t any way of stopping anyone taking a screenshot, for example. However as above the same goes, if you don’t share anything identifiable then the likelihood of anyone identifying you is slim to none.