I don’t have experience with international travel (and haven’t specifically checked ticket numbers before and after adding an infant). So my experience may not apply for you, but at least for domestic travel, the infant gets added to your reservation under “Special Services” and gets a boarding pass (with a ticket number separate from yours) The boarding pass seat says INF for the seat assignment and on Delta.com it says the person who the infant is seated with. Not sure if this changes at all with international travel with charging the 10% fare...

So basically they are associated with your reservation, will move with you if you change seats, and have a unique ticket number and boarding pass. I have never had a reason to check to see if my ticket number changes at all after adding the infant. That said, after adding the infant, the ticket issue date listed is the original issue date (and not the date I added the infant), so that would imply there was no re-issue.

Is there a reason you are worried about a ticket re-issue?