Hello:
I have a doubt. I know that “εὐσέβεια” is commonly translated as “piety”. However, I would like to know if someone could give me their translation, keeping in mind that the term “εὖ” is translated as “well”.
Would it be acceptable to you if “εὐσέβεια” were translated as “good respect”?
Thank you 
The trouble with “good respect” is that it leaves out the gods, which εὐσέβεια never does. Along with εὐσέβεια there’s ἀσέβεια and δυσσέβεια. An ἀσεβής person will get divinely zapped.
Plato’s “Euthyphro” is a dialogue that attempts to define εὐσέβεια. “Piety” is perhaps not an ideal translation, but is the best available.
εὐσέβεια was a term used quite frequently in ascetic writings. Reading what they have to say about it should give us a good head start as to what the word entails … at least within that subset of religious people groups.
Once the word gets infected by Christianity it’s not so much “gods” as “God,” of course. It continued in use in New Testament writings and I’d have thought that would make the best starting point for tracking its subsequent development.
Pity" can also be confused with “mercy”. Among the synonyms in Greek, we can find “λατρεία”: “worship”. Thank you all 
Apart from the standard piety, I’d also throw in respect on its own, without any other modifier and in a more general context, given that:
α + σέβεια → ασέβεια ¬ no respect
δυσ + σέβεια → δυσσέβεια ¬ dis + respect
In which case respectful is simply having respect , with ful playing the role of ευ, the former meaning characterised by, and the latter in a good manner.
Ultimately σέβεια comes from σέβας, meaning awe or respect as in reverence. If explicitly specific to god(s) without any room for other meanings, it can be θεοσέβεια which probably is closer to god fearing in modern English.