I would expect it's got a lot to do with celebrities, popular TV shows, films and books etc. Amelie, for example, was practically unheard of in the UK before the French film of that name was released in the early 2000s. Likewise, Luna's popularity probably has a lot to do with Harry Potter.
Sophia is an interesting one though, since its rise in popularity happened decades AFTER Sophia Loren was at the height of her fame.
Also, when a certain name gets popular, often parents consider similar-sounding names as alternatives and they rise in popularity too (e.g. Emma and Gemma in the 1980s. A current example might be Layla and Ayla, or Maya and Amaya).
One thing I have noticed is that many boys nowadays have names that end in -ie or -y (Archie, Alfie, Teddy, Freddie, Reggie...). Not nicknames but as actual legal names. When I was growing up, those names just weren't popular at all, so I wonder where that trend came from.