I appreciate that 'Aristotle' is an anglicisation of a name that has already passed through Latin and that 'Aristoteles' is closer/better english spelling. I have a passing familiarity with how 'Aristoteles' is pronounced in contemporary Greek but to what extent would if have been different in ancient greek?
Do we have a good reconstruction of the pronunciation differences between modern and ancient greek, in the way we do for Roman and Church Latin?
I'll answer the second one first. The language we call ancient Greek spans hundreds of years and several dialects from around the Greek world. There was no one "Greek" in Aristotle's day. Rather there was a collection of related dialects. You could imagine the differences between American and British English as an approximation of what it was like. A person in Sparta speaking the Doric dialect would have sounded quite different than an Athenian speaking the Attic dialect. Good work has been done to reconstruct the pronunciation of Koine Greek, in which the Bible is written, but that was spoken after Aristotle. Attic and the other classical dialects have also been reconstructed to a large degree. The book you should look at for this is called Vox Graeca.
As an aside, I'll mention that contemporary Anglophone scholars tend to use the Erasmian pronunciation of ancient Greek, which is based on a reconstruction of Attic Greek done by Erasmus of Rotterdam around 1500. This is a useful approximation, but we know now that it's not completely accurate.
So Aristotle. Ἀριστοτέλης. In Athens at that time, this would have been pronounced Aristotélēs (as wiki will tell you). The little bits over the e's mean that the accent is on the first e and the second one is long.