Yep, we're on it:) We want this to, and have gotten similar feedback from some of our beta testers. Our focus for this first version was on making the core experience of recording, retaining and retrieving names really solid. Backup/exporting is something we're definitely planning on tackling in an upcoming version.

It seems to back up to iCloud, for me at least.

Yes, iCloud should work right now, which solves the "what if I lose my phone or get a new phone" concerns. Our backup/export features will be more focused on the "I want to use my Namerick data in some other context" use case.