A ‘Vesper’ is a cocktail drink that was introduced in Ian Fleming’s novel ‘Casino Royale’. John Gruber is a fan of the James Bond stories and of high alcoholic beverages. I don’t see how the name has anything to do with note-taking, though.
Vesper is a simple and elegant tool for collecting notes, ideas, things to do — anything you want to remember. Use tags to group related items into playlist-like collections. Vesper imposes no system; organize and curate your notes whatever way comes naturally to you. Eschewing complications, Vesper's focus is on how it feels to use it.
• Attach photos to notes.
• Use drag-and-drop to reorder items. Move important ones up, inessential ones down.
• When you’re done with an item, swipe it to send it into the archive. Out of sight, but remembered forever.
Which is presumably where Ian Fleming got the name for Vesper Lynd, the love interest in Casino Royale, for whom the drink (a martini with gin & vodka [usually an either/or thing with a martini] and lillet insted of vermouth) is named.
http://en.wikipedia.org/wiki/Vesper_(cocktail)