Upvote:21
That will depend a lot on the airline and the type of ticket.
You will have to contact the airlines upfront. Some airlines do allow it (Southwest for example) but other will view it as a name change (see How to add an Infant name to an already ticketed PNR (Cryptic) — Amadeus)
On international trips, infant tickets are not always free but may still have to pay taxes and fees.
Just showing up at the airport ad trying to sort it out during check in feels extremely risky. Confirm the process with the airline upfront.