In EiraIRC's event handler, it overwrites the player's display name for ChatEvents:
https://github.com/blay09/EiraIRC/blob/master/src/main/java/net/blay09/mods/eirairc/handler/MCEventHandler.java#L185

In vanilla/Forge it calls new ChatComponentTranslation("chat.type.text", {player.func_145748_c_(), message}) which ends up using the configurable display name of the player.

ServerTools uses the display name to prefix group memberships in chat. When EiraIRC is installed, this gets erased.