"App is a free download, Google can be arses sometimes, world still spinning etc etc"
Google are always arses about it, but they needn't be.
We've dealt with Organisational name clashes before, Send letter outlining situation, other side changes name, no downtime, no stress, no fuss, everyone happy. Well, reasonably happy at least.
Google's shoot first ask questions later pylosophy needs to be fined tuned a bit. That said, Apple can be worse, they'll pass you first, then unceromoniously kill you off later.