Magiphages make theirs up, and sometimes do so while in the process of coming into existence, permanently imprinting the name into the spell in their bodies, making it an unchangeable reality for them. Some magiphage’s names are combinations of past generation’s names, they inherit them like it’s an eye color or some such, it was written in the spell material so it ended up in the mix.
Agents come up with thought-names for themselves, made up of sounds, sights, sensory experiences and feelings (basically anything that can be thought of or remembered). Other Agents shape an Agent’s name with their input as well.
Names change with the Agent, though they tend to build rather than change completely. A young Agent’s name might be just a few notes of bird song or the image of a single flower, and slowly it accrues into a complex scene, a bird perched on a dead tree singing that song in bright sunlight, that flower blooming out of snow.
Verbal Agents may try to translate this name into a name that can be spoken outloud or may come up with something totally unrelated. Non-verbal Agents often acquire names in unusual ways, and some guide the name they are given by responding to names they actually like being called and totally ignoring those calling them names they don’t like. But others just do not care, and their spoken names are about as related to them as the names we give wild animals.
Parker’s name is an example of a translation. His “real” name is something like a memory of being in a place full of trees and manicured-looking green lawns.
Smudge’s name is an example of just making something up - her thought-name is totally unrelated, she just likes the way “Smudge” sounds.
The Autumn Man’s name is an example of guiding others into a name. Since he is non-verbal, he can’t communicate what his name is or choose a translation. Humans just called him whatever they wanted to call him, and were usually just being obvious (The orange man, the man with one eye) - when someone finally called him The Autumn Man he was so surprised that someone got close to his name that he perked up and looked them right in the eye. That caused the name to catch on.