> and _all other_ product names on the store
Not true. Nobody fakes random products. It's the top scoring ones that are getting faked - for the obvious reason that this is what people are looking for. If you're not in top N (100, 200, whatever), faking you is useless, you just replacing nobody with nobody (exception may be bank apps, where even faking relatively obscure ones can be lucrative, but let's not get into niches for now). Just scanning against the top ones would kick the floor from under the most current fakers.
And of course you don't need to continuously re-scan the data - you need to scan only once, when the app is submitted or the name is changed. So, in summary, when adding app or release to the store, you need to check its name and description against a list - let's be generous - of 1000 strings and maybe run a basic text classifier if you are feel in very AI mood today. Is that impossible to scale? Nope, it's fairly easy.
> but the next day someone publishes the same app
So your argument is because simple checks are not perfect and do not cover 100% of possible fakery, let's not do anything and allow even the dumbest fakers to run free and fill the store with trash. Does it make sense to you? Because it doesn't make sense to me. Probably you decided since your argument won't be perfect anyway, there's no point to even try for it to make minimal sense?