Just for the sake of completeness, the actual history here is that Ancient Greek has the latter Phi Φ which, during the classical Greek era of around the 5th century BC, was pronounced as a particularly strong /p/ sound that produced a noticeable puff of air, as opposed to the letter Pi π which was a weaker /p/ sound. It's the exact same story with Greek Theta θ vs Greek Tau Τ and Greek Chi Χ vs Greek Kappa Κ. This distinction is called 'aspiration'.

The Romans obviously had quite a lot of contact with the Greeks and took a lot of Greek words into Latin. However, the issues is that Latin did not have these aspirated sounds natively, and so they didn't have an simple way to transliterate those letters into the Latin alphabet. The clever solution they came up with was to add an <h> after the aspirated sounds to represent that characteristic puff of air. So, they could easily transcribe the distinction between πι and φι as "pi" and "phi". Thus begins a long tradition of transcribing these Greek letters as 'Ph', 'Th' and 'Ch'.

The awkward issue is that languages tend to change over time, and by the 4th century AD or so, the pronunciation of all the aspirated consonants had dramatically shifted, with Phi Φ becoming /f/, Theta θ becoming the English <th> sound, and Chi Χ becoming something like the <ch> of German or Scottish "Loch". This was generally noticed by the rest of Europe, and other European languages tended to adopt these new pronunciations to the extent that their languages allowed, though some languages also changed the spelling (see French 'phonétique' vs Spanish 'fonético'). Plenty of languages kept the original Latin transcription spellings though, and thus we have the kinda goofy situation of 'ph' being a regular spelling of the /f/ sound in English.

So, tl;dr: Ph was just a clever transcription of a unique Greek sound that basically was a P plus an H. Then the Greeks started pronouncing it as an F, and so did everyone else, but we kept the original spelling.