Originally Posted by
Kalise
In Eorzea, Nameday does appear mean the same thing as Birthday.
Evidenced by the Custom Deliveries questline for Zhloe, wherein one of the delivery requests is based on the fact that Khloe was sad that her friend didn't have a Nameday because she didn't know her parents (So she was told she could share her Nameday with her friend so they could both receive gifts)
After which she goes on to say that all other kids that come to the orphanage who didn't have a Nameday would be able to share hers.
Meaning that, there are likely quite a few people living in Eorzea who don't have Namedays, especially after the Calamity (Which would have killed a lot of people leaving orphans who may be too young to remember what day was celebrated as their Nameday), but whom still actually have names.