If the bank were going to ask for proof of mothers maiden name there would be a large community of paranoid people (me being one

) who could not prove any connection between the name used and the actual one. In fact I don't even use the same 'maiden name' for more than one of the web sites asking for it.
It is actually recommended that you DON'T use the true name to answer these sorts of questions on web sites or with banks - for all the reasons mentioned above

The idea is that "mother's maiden name" is simply used as a reminder of the word you use.
So my first school is anything but, my favourite car is the opposite, I was born in the town of my grandfathers birth - you get the idea

Obviously if you are being asked these questions by the tax man for example you probably need to give true answers but simply for web site security no.