There are also many other large banks that omit "Bank" from their name such as Wells Fargo.
Keep in mind this is not a traditional bank, so following the rules of traditional banks would be inappropriate. They are better off following the rules of progressive startups which have been using simplicity in their names quite successfully as of late (e.g. Square).
As for Bank of America, you couldn't remove the Bank from Bank of America or it'd just be America which doesn't make a whole lot of sense. I don't think Bank of America, aside from controlling most of the banks in this country, is an objectively great brand. Rather, I thought it always tried to piggyback and sound like a federal entity which it's not and always found its name disingenuous.