I believe that Tolkien (author of the Lord of the Rings) may well have derived his name for one of the three layers of Middle-Earth air, the Ilwe, from this name.
Now, noun names are not all that uncommon in Finland. Children have been named Pilvi 'cloud', Aamu 'morning', Ilta 'evening', and the likes, and these are perfectly acceptable names, but this one gets a tad too literal and concrete for many Finns' tastes somehow. I guess this name has been quite common, but I have yet to hear of even a very old woman who has died long ago named Ilma. The masculine name Ilmari used to be common, but it doesn't really mean anything, like this one does. Besides, the name sounds like some other hideous grandmother names like Elma and Alma.
Ilma is also a very much used word in Maltese meaning Water. The Arabic word for water is Mai or Ma and Il is the article as "the" used before the Arabic word, thus becoming Il-Ma and the Maltese adapted it as one word, Ilma.