Why "Middle East" not "Central East", and Why "Central Java" not "Middle Java"
Solution 1:
Because (in the thinking of the people doing the naming) the Middle East is not 'central' to anything. It's a 'middle' amount of distance away.
In the days we are talking about the 'East' (i.e. anywhere east of Europe) was divided into three areas - the Near East (Turkey, Greece etc.) the Far East (India, China etc.) and the area in between them - called the Middle East because it is midway between 'near and 'far'. It's not 'central' because Europe is the centre (at least according to the people doing this naming). Instead it's a 'middle' distance away.
'Near East' and 'Far East' have fallen out of frequent usage, probably as being too blatantly Eurocentric. Only 'Middle East' remains in common usage.
Central Java, by comparison, really is in the centre of Java, right between East Java and West Java.