If Σωκράτης is transliterated as "Socrates", and Ἱπποκράτης is transliterated as "Hippocrates", and other Greek names ending with -ης are transliterated as ending with "-es", why isn't Ἀριστοτέλης transliterated "Aristoteles" instead of "Aristotle"?
Aristotle is the anglicized form of the the transliterated Aristoteles. According to this article on historical personal names, at one point in time many foreign language names were given an anglicized version:
In the past, the names of people from other language areas were anglicised to a higher extent than today. This was the general rule for names of Latin or (classical) Greek origin. Today, the anglicised name forms are often retained for the more common persons, like Aristotle for Aristoteles, and Adrian or (later) Hadrian for Hadrianus. However, less well-known persons from the antiquity now are often given their full name (in the nominative case).
I think that some of the anglicization may also depend on what Latin names each person was given. Though this is not, by any means, the best source, this list of names lists that Hippocrates and Hippokrates are the Latin and Greek forms of the name. Aristotle, on the other hand, is listed as Aristoteles and Aristotle.
So the conclusion I put forth is that these names were all anglicized based on other names that the philosophers were known by (here, Latin).