\version "2.21.0"

\header {
  piece = \markup \typewriter \italic \bold "Not the good piece name"
}

\paper {
  oddHeaderMarkup = \markup {
    The piece on this page is :
    \fromproperty #'header:piece
  }
  evenHeaderMarkup = \oddHeaderMarkup
  oddFooterMarkup = \oddHeaderMarkup
  evenFooterMarkup = \oddHeaderMarkup
}

\book {
  \score {
    \header {piece="Piece A"}
    {a''4}
  }

  \pageBreak
  \score {
    \header {piece="Piece B"}
    {b'4}
  }

  \pageBreak
  \score {
    \header {piece="Piece C"}
    {c'4}
  }
}