Symbols

Primary Symbols
"Like a War Machine even needs horns!"

- Klowny

Speculation
The Wayfarers randomly receiving new symbols after rebirth could represent not just rebirth, but reincarnation; being reborn with a new name, a new personality, and with memories of past lives being lost.

In Fandom
Fans will often use custom symbols for their characters. Fan characters will usually keep their symbols - and memories - after rebirth.

Black Cloaks may lack a symbol, implying that they are "soulless."

A fanmade, expanded list of symbols can be found here. Similarly, you can find a random symbol generator (complete with symbol names, based on the appearance) here.