may describe the bearer as either a good speaker or having a good rep, you'd have to be Greek to say I suppose. "Well-spoken of" seems most likely to me, and I'll trust the Greek person here.
However, the site is not technically incorrect. It is ambiguous because it gives an etymological meaning, and doesn't infer the actual translation.
"Reputation" = how someone is spoken of. It should be the same Greek root as "speak"
EF: maybe it comes out EF- if you're Greek and looking at this word, but the way we write that root in English is generically EU-. I'm sure you're both talking about the same thing: "good."
Damis, you'd be more convincing in your certainty of the meaning of Katherine
if you would quote the references, and perhaps indicate the references or research used therein. Or at least explain why it makes sense in Greek. The definition in the database gives other possible meanings that are just as convincing to laypeople who don't know any Greek, and for all we know, the research is better.