There are a few names that are water, fire, earth and air related, but these are my favourites:
The female name Cari is certainly water related. In fact, the Turkish meaning of Cari is "flows like water". You can't get much more water related than that, right? Plus, the name Cari just sounds awesome to me.
The female name Adara is my pick for a fire related name. Adara is of Hebrew origin, and literally translates to the word "fire". It's one of those names that's really pretty, but you don't often hear.
Another female name for earth is May. There were a fair few names I could have chosen for this one, but the translation of May is "the Roman earth goddess" which sounds awesome to me! I haven't heard the name May in years, and even when I did, it was the name of a very old lady.
I went with an obvious one for this one. My pick for the best air related name is Aria. The name is most famous for being an operatic vocal solo, but translates to "air" in Italian.
Here's an amazing video highlighting some of the world's luckiest people when it comes to names. Enjoy!