An “integer” is a whole number- a number that isn’t a fraction/decimal. You can have negative integers/whole numbers, and 0 is also an integer that isn’t truly positive or negative.
If you specify that you want a positive whole number/integer that technically wouldn’t include 0, same if you specify a negative number.
So if you’re looking for a value that is a whole number that is either zero or positive “non-negative integer” is probably the most succinct way to phrase it.
They can also be called “natural numbers” but depending on context, that may not always include 0.