While the original colonists followed the same first-name/last-name structure as most human cultures, that convention was dropped near the end of the first pass when it became clear that their culture had been jarred enough by Thread that they should develop their own uniquely Pernese identity. Most children are named by combining syllabals of their parents' names (thus allowing a form of heredity even through single-naming), or those of close friends, or even just making them up.
Also during the first pass, it was revealed that Dragons would slur the names of their riders when talking to each other, thus Mihall became M'hall. Afterward, riders would deliberately shorten their own names upon impression. This became known as an 'honorific,' and Weyrfolk would give their children names that could be easily shortened, assuming they would eventually become dragonriders themselves. In this way, the son of F'lon and Larna was born Fallarnon, eventually changing his name to the honorific F'lar when he impressed bronze Mnementh. There are a few exceptions; most female riders and some males don't have names long enough to be shortened, so they stay the same.
All dragon names end in 'th', and watch-wher names end in 'sk' with few exceptions. Watch-whers name themselves after their handlers, increasing the length based on how strong their bond is; unless they happen to be stationed at a major Hold, in which case they name themselves after that. They have also been known to change their names if they change handlers. It is unclear whether the gold dragons name their young telepathically before they hatch, or they just come up with one on their own. Dragon memory also doesn't allow them to remember many names of other people or places unless they're well liked, so they end up describing them instead. This can become frustrating when trying to find specifics. Ruth called Brand 'The thick man', 'Harper' was universally Master Robinton, or 'Weyrwoman' could be either Lessa or any other queen rider.