I think both
Gioia and
Joy are lovely, both in a slightly different way.
Gioia reminds me a bit of
Gaia in how it looks and I think that's because I think they have quite a similar feel to me. I think I like
Joy more, especially as a middle name, but absolutely not necessarily.
As for other names with similar meanings I like, it is
Felicia,
Felicity, our Polish
Felicja and everything related I guess,
Serena, Serene and
Serenity and Polish, but actually not used, I guess, or extremely rarely used name - Gaudencja, which is from Latin gaudium - joy, happiness. Apparently it also has other form - Gaudia - which is also very nice. And I like
Letitia too.
My PNL:
https://www.behindthename.com/pnl/154777