derives from the words EU (åõ), and FEME (öÞìç). Feme in modern Greek, In contemporary Greek, FEME means one thing: reputation. However, in Classical Greek it meant the following (and I quote "A Greek-English Lexicon", H.G. Liddell, R.Scott) it also means "utterance prompted by the gods, significant or prophetic saying" and "any voice or words, speech, saying". According to the same source (http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2345406
in Classical Greek means:
1. abstinence from inauspicious language, religious silence
2. in positive sense, auspiciousness, esp. a fair or honourable name for a bad thing, euphemism
3. prayer and praise, worship
4. honour, good repute enjoyed by men
2. On Katherine
: Here things are uncertain. Professor G. Babiniotis (Ëåîéêü ôçò ÍÝáò ÅëëçíéêÞò Ãëùóóáò, óåë. 87) suggests the the "Hekateros" derivation and considers the êáèáñüò (clean) explanation as pataetymological.
CONCLUSION: Both your, and this site's meanings could be correct.
PS please check the word Hubris, which is also Greek ;)