There is. On the sharing screen there is a matches section that shows the intersection of your lists, sorted based on a combined sorting of your favourites.

It does let you see your partners lists too however, so it’s not completely hidden.

There already is:

* https://apps.apple.com/us/app/babyname-find-it-together/id95...

* https://apps.apple.com/us/app/kinder-find-baby-names/id10684...