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Would "purely functional data structures" float your boat?

I suspect the idea is to tie in with the idea of '(purely) functional programming', which is where these will shine.

In any case the term '(purely) functional data structures' seems pretty well entrenched and dates at least to Okasaki's thesis in the late 1990s, possibly earlier (I'm not an expert). In fact, it looks like the link actually mentions Okasaki's work.

So an appeal to authority? [0] Or to tradition, I'm not sure.

[0] https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFalla...

No, not really. I'm not saying anything about what these things ought to have been called in a perfect world (though I think it actually fits pretty well). I'm observing that they've been called by this name for a while, so even if you can find an unambiguously better one, popularizing it may be hard.

I always thought it came from the well-known 'Purely Functional Data Structures' by Chris Okasaki.

Why? Fork-on-write seems very descriptive and nice, persistent seems less illuminating than immutable. Functional... eh, as someone who already knows the functional programming paradigm, I know what it means, but it would otherwise be an unhelpful descriptor.