Hi,
There is no issue with 0.
That's the number behavior.
The system returns all the products with what you enter in the field in their name regardless of whether there is something else.
So it's not only with 0. If you enter "10", you'll also get 10, 104, 1000, etc. And if you enter 104, you'll also get 1040, 1045, 2104, etc.
Now in the settings of your filter, you have the setting "Search processing" where you can configure how the search should be have.
If you set "exact", then if you enter 0 in the search field, the system will only return the product with the product name being exactly "0".