In the earlier days these were no serious issues at all.
I have always felt that we have made things unnecessary complicated now a days especially after the nineties when computerisation started and our governments started implementing what the US and other nations told us to comply.
Our authorities are still blind and deaf to our native problems for which only native solutions are to be applied. As computers use English, none of our native names can be spelt rightly the way it is pronounced. So when the native names of persons and places are written in English, the spellings change drastically according to the imagination of the person who enters it in computer.
Filling forms by self or facility to verify the whole thing before it is finally entered are all very recent developments. Earlier things were done by someone at some place and the output came later with all its mistakes and the end user could not do anything to change it. For someone's mistake we have to suffer.
When new things are implemented, generally those who had been using the earlier systems were given time to adapt and change and correct any mistakes and changeover to new systems. This is not done now. So everyone irrespective of whatever he was subjected to earlier is now strictly put under new system. In that poor, innocent, naïve and helpless people suffer for wrongs that were not their creation.
If the names of places and persons are to be recorded in the mother tongue as an addition, to verify, the difficulties will be less at least in the respective states matters.
In your case, what you have to do is to get an affidavit from Gazetted Officer, MP, MLA, Municipal councillor etc. and make at least one record like PAN, Aadhaar etc correct and use the same for all further proofs.
Another problem we face now is that everything is outsourced and those who sit at the front desk do not have any discretionary power and simply take things in 'letter' and no 'in spirit'. If each such office have some high powered officials with some discretion power things could have been so easy.
I have faced tremendous problem in applying for PAN for my son. At last in one of the offices there was someone with some good sense and advised us the correct and practical ways.(whereas at one or two earlier service places they gave simply negative answers)
In the present case,(if you are urgently required to join a bank) please go ahead with the existing documents, give affidavits for stating the correct name and saying that it is just mistype only and the person is same. Have some more records which should establish the matter. I think nationalised banks with their officials with common sense may accept the same or suggest the right practical way to solve the issue.
(I suggest to all people who face similar problems of spelling mistake, etc to write to PM for his Mann Ki bath and to take remedial measures instead of harassing genuine people)