That's true in the Bay Area at least, but not necessarily everywhere. Back when I was their customer I recall visiting NYC, and asking several random strangers if they knew where I could find a "B of A", and none of them knew what I was talking about, until I clarified, "Bank of America".
I'm a New Yorker and I know what you mean by "B of A," as do many of the people I know. I think we're both dealing with small anecdotal data sets here, though.