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.
Can you give more context to where the phrasing is used? Coming from a computer science angle, there are different data types for different things. For instance, you would use a “float” (floating point) data type to store a number like 7.12. Likewise, you use an “int” to store a whole number (such as 7). Because computers use a certain number of bits to store information, this means there’s a max size to your data. int data types specifically have a “signed int” option as well as an “unsigned int” (the latter being a non negative integer). The benefit there is that by not storing a sign, the int can store numbers about 2x as large as a signed int.
If I dont need to ever store a negative value, I might explicitly call out that when writing out an algorithm