This has by far the best discussion of the visitor pattern I've yet to come across.
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Given the syntax tree example from Wikipedia, I think I'd call it AstWalker, AstItem::dispatch(AstWalker) and AstWalker::process(AstItem) instead of Visitor, AstItem::accept(AstVisitor) and AstVisitor::visit(AstItem).
"The walker walks the AST, each items sends it to the next ones, and the walker processes them". That means something. "The visitor visits the AST items, which accept it" means basically nothing. It's more general, but also contains very little useful information. So the visitor might need different names in different situations. Fine. Just add a comment "visitor pattern" for recognizability.
I remember a situation where I needed to walk two object trees for a data comparison and import operation. I created an AbstractImporter that walked the two trees in lockstep in a guaranteed order and invoked virtual methods for each difference. It had a non-virtual doImport() for the ordered data walk, and doImport() called virtual methods like importUserAccount(), importUserAccountGrouMemberships() etc. There were two subclasses of AbstractImporter: ImportAnalyzer collected differences to display them, then there was a selection step implemented by a kind of list model + a bit of controller logic, then an ImportWorker to make the selected changes. All rather specific terminology and not exactly the visitor pattern.