Thank you in advance!
A dynamic stamp will prompt you for information at the time it is applied, and you cannot change that information once the stamp is placed in your document.
See here for a tutorial about custom dynamic stamps: https://acrobatusers.com/tutorials/dynamic_stamp_secrets
"you cannot change that information once the stamp is placed in your document."
If you select the stamp you want to change the data on and run the following script, the stamp code will rerun.
var stamp = this.selectedAnnots;
var props = stamp.getProps();
The data that you already entered won't be set in the dialog but there are ways around that too.
I should have said that there is no documented way of to change the data
For clarity... the effect of deleting the APCosObj is undocumented, the property is enumerable. You can't set it, but you can delete it forcing Acrobat to essentially reapply the stamp. Actually most of the cool stuff you can do with dynamic stamps is undocumented... by Adobe... but documentation does exist.