I asked about it on Facts once
https://www.behindthename.com/bb/fact/5415795Basically if it is bringing its sound from Greek, it'd be kha-REE-klee-a (modern Greek for sure, whether it's Charikleia or Chariklia)
or kha-REE-kleh-a (kha-REE-klay-uh, to me at least) is a possible ancient Greek pronunciation.
I guess. The answers were aimed pretty far over my head, so I hope I understood them.
Nobody answered me about there being any different, English pronunciation.
Anyway I would rather it have been as you have it, with stress on the first & third syllables, myself, but I'm not sure it is legit.
- mirfak