According to Pottermore, there is The Quill of Acceptance and the Book of Admittance, which together identify all children who exhibit signs of magical potential. According to the article
The Quill's sensitivity, coupled with the Book's implacability, have never yet made a mistake.
If so, why was Delphini not identified? Tampering seems unlikely since the book
has not been touched by human hands since the four founders placed it there on completion of the castle [Hogwarts].
Wouldn't that have meant her name would appear and she would be sent a letter to Hogwarts, thus everyone would know about her?