"Dennis" is the modern worn-down form of Dionysius.

Most of the rules about Catholic naming were Reformation era. On the one hand, that didn't affect the Greek Orthodox. On the other hand, many early saints became Christian only in adulthood and had names like Demetria or Apollonaris, and never thought twice about it. Thirdly, I generally find Greeks using non-pagan sourced names by numbers. Fourth, for them it's heritage, as it wouldn't be in most of Europe.

Names like Constantinos, Iannos (John), and Viron (Byron) are much more popular than Herakles, Pollux, or Apollo.

Source: Ingraham, People's Names

In Ireland, Catholics have often used names from Irish mythology, as well as ones from the Bible. "Pagan" names like Aoife, Oisín, Fionn, Deirdre, Conchúir/Conor, Diarmuid/Dermot and Medhbh/Maeve are really common. These are the names of heroes, queens and sorceresses from mythology.

I was also raised Catholic and never heard anything about "pagan"names being bad, so it must be a more specific cultural thing. Here, these names are seen as a part of Irish culture and heritage. I imagine it is a similar story in Greece.