While I also don't think Birdychat is a good name, you could also argue that "Whatsapp" is a weird name for an app billions of people use.

WhatsApp is a bizarre name, and I think that contributes to it occupying a "lower rent" space than the others (the goofy chat background also helps). But I think most people ultimately gloss over the joke and it just becomes kind of abstract.

With BirdyChat though, it feels like you'll be confronted by its silliness in perpetuity.