It began in 1904 as the Bank of Italy by Amadeo Giannini in San Francisco, California. After merging two banks together to form the Bank of Italy and America in 1916, it was shortened to the Bank of America in 1929. It managed to branch out of California in 1967. And it had its own credit card, the BankAmericard. That became Visa in 1975.
With all the bank mergers that took place in the last thirty years, it isn't a wonder that the Bank of America was bought by the former NCNB (North Carolina National Bank), when it was still known as Nations Bank. Since the Bank of America was an older and more reputable institution, it took on that name.
It's not the same as the Bank of America that existed when I was younger. That was a California bank. It's now based in North Carolina.