For instance, the Greek word ψυχή is always transliterated into English as "Psyche", which is completely wrong, if one pronounces it as the English letters are pronounced. Yes, the Greek uppercase is Υ, which looks exactly like the English uppercase "Y", but the Greek letter is always pronounced u and ψυχή should be pronounced "psuche". How did this odd mistake come about and why has it persevered for so long, even in scholarship.
The Y is a letter imported to the Latin alphabet from the Roman one in order to accommodate the Greek names that had the ypsilon, which is not the same as a Latin "u". The Greek "u" in ancient times was pronounced as the modern French "u" or the German "ü". However, with the evolution of languages, nowadays the Greek ypsilon is pronounced the same as the iota, the eta, or the digraphs epsilon-iota and omicron-iota. The transliteration for a "u" would be omicron-ypsilon
So, ψυχή would today be pronounced "psikhí", but in antiquity it would have been pronounced as "psükhé".
Anyhow, I am paging our resident u/KiwiHellenist for this, though I think this would be more of a question for r/asklinguistics instead of this subreddit