There no easy, convinient mod that displays an object's unlocalized names (string IDs) in a tooltip like WAILA.
MineTweaker is probably the easiest one to use if you want to get string IDs in game quickly. With simple chat commands you can display info about objects you are looking at or holding in your hand. Or just make a list of IDs of everything currently installed in the game in a log file.
I think they mean the item's/block's registered name (unlocalised and registered names are two different stories).
It you want to view all registered blocks and items, just use the auto-completion for the /give command.
No idea why it doesn't work on the server, perhaps it's a limitation Mojang put in place? But AFAIK all commands are handled client-sided until you actually send them to the server, so pressing Tab AFAIK is handled by the client. So Cauldron shouldn't be affecting it.
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Author of the Clarity, Serenity, Sapphire & Halcyon shader packs for Minecraft: Java Edition.