Hello PJL57,
We'll be happy to help out with updating your contacts so they will display a related name. You can do this both in the Contacts app and Phone app.
It sounds like you know how to edit, so for reference, here is the link to Edit contacts on iPhone.
Open Contacts app > select a contact > tap Edit > scroll down to "add related name" > type in the name you will want Siri to recognize, for example "Son" > tap the link to the left of name you entered and select the relation (so you will see son > Son) > tap Done.
It would be the same steps using the Phone app.
Following these steps should update the relation for you. Let us know if you still have trouble.
Have a great day!