I actually quite like that naming convention.
Well, yes, it works quite nicely on a fantasy game. Not so much in real life where I bet it kinda sucked...
Another naming convention to take in mind -though it requires a developed ingame zodiac/calendar-. In the ancient Anahuac people would have four names: the first a calendaric name based on the day of birth (or naming ceremony if it was a particularly unlucky day), the second a given name as chosen by the parents -though most of the time it was after their totem animal-, the third one a nickname used by close family and friends, the fourth one a secret ceremonial name known only by you, your parents, and your local sage that marked your fate and calling in life. This was some kind of magical/ceremonial name that was a great deal, so nobody but the gods as meant to know it.
For example legendary emperor and founder of Tollan: Ce-Acatl Topiltzin Quetzalcoatl, Ce-Acatl was his date of birth -a day that predicted both great glory and great calamity-, Topiltzin -Our Lord- was his given name, Quetzalcoatl was his secret name. Of course revealing your secret name was a bad idea, as shown by his fate, as he got drunk, committed incest, desecrated Quetzalcoatl's temple and left Tollan in disgrace swearing to return one day. (If this sounds exactly like the legend of Quetzalcoatl is because it is essentially the same legend. Whether he was an historical figure that faded into myth or a purely mythical construct to begin with, later oral tradition confounded and identified him with Quetzalcoatl the god, just to reinforce how big of a deal secret names were.)
The calendaric name convention is also the reason indigenous people and Mexican people in general up to the later half of the 20th century embraced the European custom of naming people after the patron saint of their birth date. It was just a matter of replacing one calendar with another.
As for the totem animal, in some regions the father of a newborn would mark a circle with cal on the ground and the first animal to leave its footsteps on the line would be the totem animal and added as another name to the child. Of course it later got ridiculous when Pedros Bicicleta and Marias Carro started to pop up...