Yes if using Paypal or Revolut for example your name will be visible by the other party,
but thats all, no other personal details are visible.
So HodlHodl and PeachBitcoin are as close to private as is possible going online.
There is the option of trading face to face, thats anonymous but has its risks too.
A trade done on this forum is essentially private - even though admins here can give your info to authorities if they are under subpoena.
Honestly being completely anonymous is like a holy grail, you can cut down your traces but cannot completely eliminate them. As long as you are not getting involved in criminal activity like money laundering this forum marketplace can be used - make sure to use a trusted escrow, too many scammers lurk here.
Dont fall into the paranoia of privacy with crypto. If you are clean you have nothing to worry about.
Yes I agree, especially with Bitcoin if it isnt illegal in your country there is no need
to get hung up too much on 100% privacy/anonymity.
Obviously we all have to exercise a degree of privacy but being able to limit it
to only giving your name away is ok IMO.