Is the name of the famous conqueror of the Aztecs Hernán Cortés or Hernando Cortés? And how did the discrepancy occur?

While he is often now referred to as Hernán or Hernando Cortés (IPA: [kor?te?]), in his time he called himself Hernando or Fernando Cortés ([kor?tes]). The names Hernán, Hernando and Fernando are all equally correct. The latter two were most commonly used during his lifetime, but the former shortened form has become common in both the Spanish and English languages in modern times, and is the name by which many people know him today.[1] Although his paternal surname is sometimes spelled in the Anglo-Saxon world with a final "z" as Cortéz, this is incorrect. Cortéz is a Spanish surname but in Castillean Spanish the letters z and s represent different sounds, and the names also have different etymologies. Cortés' family was distinct from the families using the spelling with z, and he did not use this spelling.

https://en.wikipedia.org/wiki/Hern%C3%A1n_Cort%C3%A9s