Question: In Judith in Vulgate, why does Jerome transliterate the name "Arphaxad" with 'ph', but he transliterates "Holofernes" with an 'f'?

By the time of Jerome, both 'f' and 'ph' were the same sound, the English /f/, right? And Greek letter φ was pronounced /f/ as well at the time, right?

Regardless, they were arguably the same sound given that Jerome was transliterating φ from the same Greek text two times.

Answer: 
### Both of these names are older than the Book of Judith, and come from different places.

*Arphaxad* is a transcription of Hebrew אַרְפַּכְשַׁד (*ʔarpakšad*), which appears in Genesis: a minor character who's only mentioned in genealogies.

*Holofernes*, on the other hand, is the Persian name of a Cappadocian ruler mentioned in several historians (as *Holophernes*, *Olophernes*, *Orophernes*); I haven't been able to find the actual articles, but I've found citations for Justi 1895 and de Jong 1999 linking this to Iranian \**Varufarnah* "having wide glory" (related to Avestan *Xvarenah* "Glory (deity)")

Jerome, as a rule, stuck very closely to the Greek of the Septuagint when transcribing Hebrew names; that's why we see *Jose**ph*** for Ἰωσή**φ**, even though the Hebrew of the time had an `/f/` at the end.

But *Holofernes* wasn't a Hebrew name, and presumably it had been previously transcribed into Latin—the only surviving mentions I could find are written in Greek, but the historical Holofernes lived during the Hellenistic period and made treaties with Roman rulers. So instead of just copying out the Greek and getting something like *Olophernes*, Jerome went with the Latin transcription he was familiar with.
The answers provided by cmw and Draconis are very learned, but I'm not sure they explain the inconsistent ways of transliterating Phi in the Vulgate. Here is why.

1. Different editions of the Vulgate transliterate Phi in different ways. For example, the Clementine edition has *Arphaxad* and *Holofernes*, which is what FlatAssembler asked about. However, the Stuttgart edition of the Vulgate has *Arfaxat* and *Holofernes*.
2. I am sure that the answers given about Hebrew and Aramaic are correct, but I'm not sure they are pertinant, because Jerome almost always transliterated proper names in the Old Testament from the Septuagint, even when he translated from Hebrew or Aramaic.
3. My own answer is pure speculation. The medieval manuscripts of the Vulgate were written by scribes who were listening to lectors reading from earlier manuscripts. The scribes wrote what they heard, and they heard what the lectors said, not what Jerome wrote. So the details of Jerome's transliteration of Greek Phi have been lost in history.

I suspect that if we want to understand why *F* is here and *PH* is there (and *D* and *T*), we will need to study the state of classical and biblical scholarship during the Early Modern Period when the first bibles where being printed. I am far from an expert in those subjects in that period.