No, the whole word KONEO doesn't mean anything in Japanese, but depending on how you pronounce it and where you place the accent, some Japanese people might wonder what it means for the following reasons;

"kone" in Japanese means(if KONEO is pronounced like co-neh-o and the accent is on the second syllable):
1) connection
2) part of a verb "koneru" (to knead, to work clay, to argue for argument's sake, etc.)

O is often used at the end of a boy/man's name(ex. Yasuo, kazuo, etc.), the whole name could imply something like a connection boy.

If KONEO is pronounced like co-knee-o and the accent is on the first syllable, then I don't see any potential problem.

As for what it might mean in Greek, I do not know and I suggest you pose this question on the Greek-Japanese ProZ site.