Yes, basically Greek words in English are pronounced as Latin loanwords, according to how the Greek words would have been pronounced in Latin around AD 1 (except that ph and th, but not ch, are pronounced as fricatives in English). Greek αυ and ευ were still pronounced as diphthongs at the time.

My name is Ελευθέριος and I transliterate it as Eleftherios in English.

There's a "standard" way of how greek words should be transliterated in English (ELOT 743). You can test it here https://www.passport.gov.gr/passports/GrElotConverter/GrElot...

And yes, Eleftherios is the correct transliteration :)

I know. I've even seen my name written as Eleytherios.