Believe it or not, I think it was YT where I got Bella's name. I was doing some research on the breed and kept returning to YT for information. I saw "Bella" so many times that it rather stuck and I really liked it. I had no idea I would become a participating member of the forum at the time.
We have 4 birds; Jasper and Fiona and also Pheonix and Ivy that were named from baby name sites. Our former miniature schnauzer was Brittny and our former sun conure was Mercedes. I think names are intensely personal and what I tend to like my sister doesn't.
I agree with the other posters about finding a theme you like. Nature, colors, cars, favorite books and places are great starting points. As for the Greek theme, Bella was almost Athena...
Good luck!