There's no such thing as "traditional" warrior names. Instead, naming trends in the Clans go in and out of popularity, much like human names do!
For a couple years leading up to Rusty joining the Clans, and all through "The Prophecies Begin", names emphasizing some physical characteristic were very popular. This is probably, in part, thanks to the rise of leaders with names like Tallstar, Crookedstar, and Raggedstar. This is also why some of the elders chose to change their names to reflect their appearances! Color based names were particularly in style- it was considered simple yet elegant to name a kit after a color.
Plant and animal related names were fashionable through the New Prophecy and Power of Three arcs. Naming kits after their physical appearances became considered uncreative- if you could only list the obvious about your kit, you must not be a very attentive parent...
The Power of Three and Omen of the Stars arcs also saw some movement away from the old, body based suffixes, and a shift towards more abstract names. (ex, LionBLAZE, HoneyFERN, CrowFROST, IvyPOOL, RedWILLOW) With the Clans growing to be larger in size than they had been for a long time, unique and catchy name combos became the go-to to help new warriors stand out from the crowd. (A lot easier to remember a name like Sunstrike of WindClan than Petalfur of RiverClan, right?) This trend started in ThunderClan, as they were the biggest Clan by a long shot, but it spread a bit to the other Clans as well. It caught on best in ShadowClan, while RiverClan and WindClan names remained a bit more old fashioned in general.
For the first half of AVOS was marked by a rise in monosyllabic prefixes. This trend also started in ThunderClan, mostly as a reaction to the flashy suffixes Bramblestar seemed fond of giving his warriors. No one wanted to have a warrior name that was too much of a mouthful to be chanted easily. This trend DID take off in the other Clans as well. It's also worthwhile to note that in RiverClan, it became very popular to give kits prefixes currently in use in one of the other Clans. The other Clans have no idea why it started, but there were some accusations flying around that RiverClan was trying to "steal" prefixes from other Clans, which doesn't make much sense.
Towards the end of AVOS and the beginning of TBC, a new fad of naming a kit something "lively" or "energetic" took off. It wasn't common to name kits this way before, but with the influx of unusual names from SkyClan and the new ShadowClan members Tigerstar II brought back with him, all the Clans suddenly wanted to break away from their old naming conventions a bit. This resulted in prefixes like Snap, Flip, Hop, Pounce, Whistle, Flutter, Splash, etc.
The most "poetic" naming era in Warriors history was a bit before Bluestar's time- Tallstar and Yellowfang were born into this time period, where prefixes could really be whatever as long as they were paired with an exciting, creative suffix. Some of the names considered most beautiful during this time were: Mistmouse, Meadowslip, Sandgorse, Featherstorm, Silverflame, Toadskip, Brightsky, Ottersplash, Mudthorn, Brambleberry, Moonflower...
I was just thinking about this bc of all the debates that happen in the fandom over whether or not the names of characters are good or bad, traditional or cheesy... this was just my way of making a fun explanation for the authors' inconsistency in naming the cats over the course of the series.