These days, unfortunately,very few schools in UK offer Latin and far fewer are able to teach classical Greek.
[An echo of Ben Jonson's words to Shakespeare ('Thou hadst small Latin and less Greek') perhaps!]
Consequently, how the 'well-educated, well-read' members of the present generation (the Chi players of the future!!) will learn the Greek Alphabet is not at all clear.
As Jancsika says, many of the names of the Greek letters have become known to English speakers in other ways, but I am not convinced that (of those Greek letters spelled in English with four or more letters) 'kappa', 'omicron', 'epsilon' and 'upsilon', for example, would be familiar to someone without 'a classical education'.
I'm all for consistency when it comes to classifying words in Chi, but I'm not sure it is appropriate here.