Is the Modern Greek letter beta (Ββ) pronounced “b” or “v”?

To make explicit what others are hinting at: it is pronounced /v/, but is often transliterated as /b/ for consistency with ancient Greek. You won’t see it with modern names, but you may see it library catalogues, for example, which often use the same transliteration for ancient and modern Greek.

And if a name is ancient, or entered English via classicists, or someone is being pretentious, b will be used. So for example Basil, Rhangabe, Bryennius.