You got me curious as to which states require ID to pick up prescription narcotics as I've never heard of this living in Illinois and Colorado. Turns out each state has its own set of unique and sometimes bizarre rules:

https://www.cdc.gov/phlp/docs/menu-pdil.pdf

That depends on stat, I suppose.

In my state, none of those require ID if a prescription.

Pseudoephedrine does if purchased without a prescription.

...in your state. This is not a federal requirement.