I doubt most people will know or care what Nostr is for quite a while. Unfortunately, things would need to get pretty Orwellian in my opinion. Most people will probably make associations with whichever client gets a lot of seed money and appears to be just another big social media platform with cool features. I suspect such a client will custody keys as well for users.

On the flip, I hope I'm wrong. But this seems to be the case for Bitcoin, which is similar.

It's an okay logo. I just doubt it will matter as much as some people think. Client logos will probably get more attention.