For the life of me, though, I haven't been able to remember the name the last couple time's I've wanted it (and my bookmarks are horrendously disorganized at the moment), and googling different iterations of "white noise generator sliders people birds rain" didn't yield success. I need to stash this away somewhere I won't lose it...
I have actually wondered about the name thing. It is a little whimsical, and I guess it would be easy to mix up with lots of similar descriptions like "a quiet buzz" or "a gentle burble". From that perspective, it might have been better to choose something more memorable.
The site won't rank well in google for descriptive terms because it doesn't contain a lot of text. Even for terms it does contain, it doesn't do very well (e.g. it ranks at ~20 for "ambient noise" in google US). I haven't worried about that so far because the large majority of the traffic is direct, social or for the exact term "a soft murmur".
Based on your other comments it seems like you really know what you're doing in these spaces. I'm no expert, but based on all the positive feedback, capturing organic search traffic could help you kill it. Show them and they'll stick.