As a sanity check it’s not a bad system. If you’re expecting you send money to a John Doe it makes sense to be able to tell the bank this so they can compare and come back with “uhh this account is owned by a Mary Sue, are you sure?” As far as catching mistakes I’m sure it’s fantastically good. The odds that a mistyped account number happened to land on someone with the same name is probably vanishingly low.
And that really seems to be all this is except that it uses the naivest process to do the check.
If we're willing to deal with the 'wardialing account numbers' factor, I think the right flow is "enter account number, SHOW associated name, and make customer confirm it (i. e. by transcribing it off the screen if it's a huge transfer, or just click "Yes, I meant to send to Scamco Ltd.") That avoids the usability nightmare of "the name on file is wrong but not in a guessable way."
I have pretty close to the simplest case for Western-style names-- no middle name, no hyphenation, no suffix or odd prefix, short, common first name, dictionary word last name. The number of times it gets recorded wrong is unbelievable.
The bank numbers we use in Europe (IBAN) have checksums so you will probably not end up sending your money to a wrong account (at lrast if you type one wrong digit or invert two digits).
And that really seems to be all this is except that it uses the naivest process to do the check.