Here are your options:
Even on the fast-revolving carousel of Greek finance ministers, we haven’t come across this problem for a while. Yanis Varoufakis’s name seemed to be anglicised (or, to be more precise, romanised) the same way the whole world over, from the Wall Street Journal to Paris-Match, and the brief tenure of the now-departing Euclid Tsakalotos didn’t seem to cause any major problems. But five minutes of puzzled Googling for a short news story has thrown up any number of transliterations for the new man, Manchester-based academic Γιώργος Χουλιαράκης. The ECB says approvingly that “he knows what he’s doing”. Let’s hope, during his brief tenure until the Greek elections, that we look like we do too.
House style is always important to a certain extent – consistency of spelling and word choice all add subliminally to the authority and tone of a publication’s work. But transliterated proper nouns is where it really matters (and, simultaneously, where it’s hardest to be consistent). English-speakers not familiar with Greek nomenclature might well assume that Yorgos Houliarakis and George Chouliarakis are two different people with similar names in Athens, just as many might still be unclear that Deir ez-Zour and Deyr Azzour* – another notorious pitfall for transcription – are one and the same place in Syria. God bless Google – it finds all the variations whatever you search for. But that does mean that you can be deceived by confirmation bias when you hurriedly paste the reporter’s spelling into the search box and see it come up with hits.
It’s a hard problem to solve. You can set some general rules for transliteration, as the Tribune’s style guide does in a 600-word entry on Arabic names, but even that starts off by admitting “there are dozens of ways of writing the former Libyan leader Muammar Gaddafi’s name in English, and a reasonable argument can be made for adopting almost any of them”. The only real solution is to pick a style, notify everyone and keep a long and growing list of romanisations available for the copy desk to refer to. It’s a fiddly, awkward, case-by-case approach that can’t be replaced by rules or “common sense”, but it’s worth it: because otherwise you can cause an awful lot of confusion without ever being wrong.
* Or Deir Ezzor, or Deir el-Zour, or …