What was the full name of the king archon from Euthyphro, who condemned Socrates to death?
"Archon basileus" translates as "king magistrate" So says Wikipedia: https://en.wikipedia.org/wiki/Archon_basileus Socrates's trial does not seem to have had a presiding official in the sense of an American trial judge. https://en.wikipedia.org/wiki/Trial_of_Socrates
Euthyphro was a character, with Socrates, in Plato's Euthyphro dialogue. The full surviving text of the dialogue is available at The Internet Classics Archive: http://classics.mit.edu/Plato/euthyfro.html