This is about two related issues:
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The graph name is taken to be the folder name. It’s pretty inconvenient for typical directory structures like: project/notes, project/logseq, etc, since the name would be notes, logseq, etc. for every project.
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The switch-to-graph menu shows the parent folder also, like in project/notes, project/logseq. I guess this is done in order to address the previous problem. But then it’s inconsistent with the name actually shown after graph switching.
I propose to simply be consistent and also show the parent folder as part of the graph name, so more context is provided.