#nostr is not an installable app. Its apps have their own logos to show on the screen. The little ostrich carachter at the end of #nostr is enough, the apps need to implement the setting to show it like consistently. Then it will have it's own code to appear everywhere the word is written.

That's a nice logo for an application that uses Nostr, but protocols don't really need or have logos. The recognition comes from the brand or the application that uses the protocol.