It's a baby name generator, there's no need to track everything!

You're not thinking of the potential here. Just imagine a baby name generator that tracks its users preferences and automatically registers domains and social media accounts which it then tries to sell you.

...it sounds horrific, I'm glad OP went with this model.

They could also stand with their decision, to stick it to all the user apps, that track you to oblivion ;)

It is possible to collect information, use it locally, and not upload it to a server.

of what relevance would such data be to the user who generated it?

curiosity!