The only **unofficial** names for 3rd and 4th sons in use appear to be **spare** and (less commonly) **spare to the spare**. There are many online sources (both history and non-history) using **spare** for third, fourth, fifth etc sons, and in the UK these now include daughters.

*[Unexpected Heirs in Early Modern Europe: Potential Kings and Queens][1]* (Valerie Schutte, ed.) uses **spare** for King [Henry III][2] of France, who was the fourth son of [Henry II][3] of France, and also for [Gaston][4], Duke of Orléans, third son (though 2nd surviving) of [Henry IV][5] of France.

The [Historyextra][6] site mentions *...plus at least one spare in case of accidents* while **spare to the spare** is used with reference to Prince Edward, 4th son of Elizabeth II in [this (not very historical) book][7].


  [1]: https://books.google.com.ph/books?id=XzU7DwAAQBAJ&pg=PA181&lpg=PA181&dq=%22spare%20prince%22&source=bl&ots=qj5PY1yriS&sig=ACfU3U2i8yu3WTClUzcH41vur6KqMRci9A&hl=en&sa=X&ved=2ahUKEwjPo_C4rpPhAhXHgI8KHTOSB4o4ChDoATAIegQIAxAB#v=onepage&q=%22spare%20prince%22&f=false
  [2]: https://en.wikipedia.org/wiki/Henry_III_of_France
  [3]: https://en.wikipedia.org/wiki/Henry_II_of_France
  [4]: https://en.wikipedia.org/wiki/Gaston,_Duke_of_Orl%C3%A9ans
  [5]: https://en.wikipedia.org/wiki/Henry_IV_of_France
  [6]: https://www.historyextra.com/period/medieval/how-to-raise-a-royal-with-tracy-borman/
  [7]: https://books.google.com.ph/books?id=aThwDwAAQBAJ&pg=PA41&lpg=PA41&dq=%22spare%20prince%22&source=bl&ots=yv-UaN0S-f&sig=ACfU3U3Q-jeg4uFOPHWOPfywfRojJWxDKg&hl=en&sa=X&ved=2ahUKEwjPo_C4rpPhAhXHgI8KHTOSB4o4ChDoATAFegQIBBAB#v=onepage&q=%22spare%20prince%22&f=false