The Spanish V is usually softer and easily confused with a B. But, it might vary by country, and your Spanish is probably Spain Spanish, while mine is Latin American. The B and V are almost interchangeable. For instance if a Spaniard saw the city Havana or spelled Habana, they would say it the same. It is spelled both ways depending on the country spelling it. Also, in Spanish even the B is softer than in English. Both V and B in Spanish the lips don’t quite meet as opposed to in English the sounds are much more definite and clearer. But, again, I think it varies somewhat by the Spanish speaking country.
I figure maybe this is how the name Bill is short for William, but I don’t know it for a fact, maybe @DominicX does. Since W and V are so similar in some language and B and V in others, I assume that there might be some sort of logic there to explain the nickname.