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.

http://en.wikipedia.org/wiki/Vesper_(cocktail)

The app is sold by Q Branch LLC

Yes, which is the company Gruber started with his friends. The kid in all the app’s screenshots is Jonas Gruber, John’s son.

Like Vesper, the name ‘Q Branch’ also refers to the James Bond franchise (Q is the mastermind who provides James Bond with all of his clever gadgets).

http://www.macworld.com/article/2040883/meet-vesper-a-notes-...

There's more info on the appstore:

Collect your thoughts.

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.

https://itunes.apple.com/us/app/vesper/id655895325

I was disappointed, as well. Looking forward to reading more about vesperapp. (I've just set up a Google Alerts for it).

Vesper means evening or evening prayer

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.

Vesper Lynd is a pun: "West Berlin", spoken with an accent.

Well there you go.