During the time between children coming to live with you and the final legal adoption being granted, they will still have their birth family surname. If the issue has not already been addressed by their previous carers, it may be worth considering changing or replacing their social media accounts. While this may cause upheaval for any friends they have, it could help protect them from birth family members finding out their whereabouts.
Once the adoption is legal, the child’s surname is changed to your family surname. At this point it becomes harder for the birth family to search by name (unless the social media profile already existed and has simply been updated). New social media accounts should then be very difficult to trace by name alone.
Note that simply changing or removing the surname on an existing account will not hide it from anyone who already knows about it. That is, if someone finds and bookmarks a Facebook account, they can return to it again even if the name has been changed. Creating a new account may solve this issue, although if someone has scoured a child’s friendship group it may still be possible to find the new account. Effective Privacy settings can help.