Problems:

• BungeeCoord chat (muting) plugins prevent the chat message from reaching the Minecraft server. We therefore cannot detect the chat input for (muted) players.
• Chat input is meant to not be sent to other players, so we also need to cancel the chat input on the proxy to prevent the chat plugins there from forwarding it to other players.

Possible solutions:

• Add a /shopkeeper rename <shop> <newName|'-'> command. However, any other (future) editor options which would usually want to make use of the chat for text input would also need to provide their specific fallback commands.
• Or a more general /shopkeeper input <text> command that can be used alternatively to the chat-based text input. Even more general/shorter commands like /i <text> would be more likely to conflict with other plugins.
  However, ideally I try to avoid adding commands for anything player shop editing related.
• Those BungeeCord chat (muting) plugins could implement the muting or global chat forwarding on the actual Minecraft server instances (unlikely to happen..).
• Using some other kind of text input provided by Minecraft (signs, books, anvils, ...). However, it is not yet clear which of those would be most suited for the type of text input we want (e.g. except for books, they are too limited in the length of text they allow to be entered).
• Use the naming-of-player-shops-via-item feature (only works for player shops).

There is another open issue in relation with BungeeCord chat plugins: The chat message also needs to be cancelled on the proxy so that the chat plugins there don't forward it to other players.

I updated the BungeeForwardCancelledChat plugin accordingly to add this capability, but while testing this I ran into an issue related to the signed chat feature of MC 1.19.x when I cancel individual chat messages.

I created a small BungeeCoord+Spigot plugin that forwards cancelled chat events from the BungeeCoord proxy to the player's Spigot server: https://www.spigotmc.org/resources/bungeeforwardcancelledchat.88941/
In my very brief testing (muting players on the BungeeCoord and then renaming shopkeepers), this seems to work.