Naming
Names mean things in our culture; we don't just give them out like candy when babies are born.
Execution
Pups are not given names until they have shifted, to ensure that they will live to adulthood and to give those around them a chance to know them. (Nicknames, however, are very common placeholders to help disambiguate which pup is being discussed. These can be based on physical characteristics or demonstrated preferences, such as "Space" after particularly dark blue or black skin, or "Weld-Eater".) The first name a Stenza receives is chosen based in part on what the newly-shifted child is willing to answer to, as well as the customs of the droga, with help from clan elders.
For some, they retain the same name through adulthood, but others may take on new names after significant life events. T'zim-Sha's name was changed to its current form after the Clan Killings, when he survived the near-total extinction of his clan (and is a reference to Lan'tha's ability to raise corpses to resume battle). Ta'zhen took a name indicating her relatively small size upon completion of the Citizenship Trial (it was once used to refer to her derisively by T'zim-Sha himself; she considers it the truth).
Note: Periodically a natural mediator will be named Iradae, after Iradae, who is known for his ability to reason with his notoriously hot-headed mate Lan'tha. Notable examples include Iradae the Lawgiver. It is exceedingly rare, however, for Stenza to be named after other gods, suggesting that in the ancient past, "Iradae" was more of a title than a name.
Additionally to a name, a person may take on epithets or titles based on noteworthy accomplishments. The aforementioned Iradae the Lawgiver, for example, is widely known as such due to his role in the Battle with the Stone Menace and subsequent formation of the Unified Stenza Clans. In more modern times, An'hulla is called "Empire Builder" due to her reform project and commissioning the original Lawgiver as a show of force and power. (Ta'zhen is sometimes referred to by the phrase Èẓět’ǔ, "enduring", although this does not count as a proper title.)
In written records, Stenza names are followed by two to three determinatives, symbols which are not pronounced but which designate clan and species of origin, as well as some other noteworthy information.
In cases where the name of the individual changes, the original or previous names are functionally forgotten, scrubbed from records and replaced with the updated name.
Participants
The choosing of a first name involves the largest number of people: the person to be named, a droghi, and one other party who has had some experience with the child in question (periodically, daylight births may be named with aid from a religious expert).
Subsequent names are taken on in a declaration by the person in question, or occasionally a blood sibling or other person who was present for the noteworthy life event. If the latter, the individual being named must agree to the choice.
If, in extreme cases, a child must take on a new name before reaching adulthood, a clan elder must be present in order to help name the child (an act which frequently doubles as emotional support).
Observance
First names are typically given during the month Long Night, although it is not unheard of for this to occur at the outset of Migration.
Any additional names are taken at any point in the year, however, although the pious tend to favor First Sunrise as a time for naming themselves.
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Great tradition! My Zeribians have a similar tradition, where the children are given nicknames until they turn seven, in order to protect them from demons that might try to attach to the vulnerable children, and also because young children often die anyway :P But I might have to consider your idea that the children wouldn't have any names at all... https://www.worldanvil.com/w/salan-tuisku/a/second-naming-ritual
There's a lot of precedent in preindustrial cultures for a whole host of customs around not naming your kids right away, from the idea that they will be spirited away and swapped with changelings to the simple fact that a good number would not survive to adulthood. Although because of modern medicine Stenza children are surviving childhood, the custom persists, in part because it is believed that giving a child a name before they are known by the community is imposing a personality onto them, and it's better to wait until their personality is more developed first.