Pickle, relish or kraut, and what you may call it
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A name is a claim
A statement of identity has to describe the product accurately. That is the whole requirement and it is less restrictive than people fear, but it does rule out the thing most makers want to do, which is to name a product after the thing it resembles rather than the thing it is.
The clearest case on this property is the fermented one. A product called a sauerkraut sets an expectation about how it was made, and a quick-pickled shredded cabbage is a different product however similar it looks. The same applies to kimchi, which buyers generally expect to be live.
Relish is a useful answer to a quality problem
Hollow cucumbers, odd sizes and the tail of a crate have to go somewhere, and a relish is a legitimate product rather than a way to hide seconds. The decision worth making in advance is which of your output is relish by design, because the version of that decision made under pressure on a packing day is the one that puts second-grade product in a premium jar.
Live or not is part of the identity
If the product is sold as a live ferment, processing it changes what it is and the label has to follow. This is the commercial end of the live-or-shelf-stable decision: it is not only a logistics choice, it is a choice about what you are allowed to call the thing.
Decide before the label, not after
Every one of these interacts with the statement of identity, the net weight and the ingredient list. They are cheap decisions on paper and expensive ones after a print run.