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The answer is more obvious than you might assume: they did not, in fact, have "English" sounding names.
Rather, the names of the more famous ancients have been anglicized by later English authors, for ease of reading by an English audience.
"Alexander the Great" was actually called "Ἀλέξανδρος ὁ Μέγας" or "Aléxandros ho Mégas" in the Latin alphabet. His father "Philip" was called "Phílippos." Not quite as familiar, eh?
If you read grab any book on ancient history off the shelves, or any translation of a work from antiquity, you'll often find an author's note somewhere in the preface or above the index where he relates how he's dealt with the problem of names. To take a book I was using for an earlier post:
"Names are given in the forms in which they are commonly encountered in modern English." — Peter Salway, A history of Roman Britain
There's also a second factor in play: the names of these very famous and succesful people were emulated by people in later ages. You'll find that the history of Europe is overflowing with people, including many nobles and rulers, called some version of "Philip" and "Alexander." After all, everybody likes to be named after a winner. I shudder to quote Wikipedia, but to give you an idea: [this page](https://en.wikipedia.org/wiki/Philip_(name)) lists an impressive 43 different kings and rulers named some variant of "Philip."
This is the second reason these names sound so familiar to you: they have been copied so much you've become used to the way they sound, even though their root is from a very different language than your average Tom, (Thomas, originally Armaic, came this way via the bible.) Dick (Richard, originally introduced by the Normans) and Harry. (Harold, originally Old English or Old Norse.)
If Perdiccas had gone on to conquer much of the known world, I suspect that nowadays we'd encounter a lot more people named Perdick.
You're asking why some Greek names like Alexander and Philip (and George, Andrew, Nicholas, Christopher and many more) got popular in modern English, while others didn't?