Name mismatch in company profile name

It is better to get the name corrected. Your PSU might not have raised any objection. But later at the time of retirement, you have to claim your retirement benefits. It may become a problem at that time. What is the name of your PF account? Are you filing IT returns? What is the name on your PAN card? What is the name on your Aadhar Card? If all these are matching, there will not be any problem. Otherwise, you should get it corrected on your company

You can contact your HR/IR department and discuss with him the problem in detail. The concerned person may know how to get these corrections to be made. You can follow his advice and do the needful so that the name will be corrected as per the name on your other documents.
Before doing that he may ask you to get an Affidavit made. Your company will also have a legal advisor. You can contact him also and he will guide you properly on this issue and you can get an affidavit made as per his direction and can be submitted to your company. Then it will become easy for them to change name correctly.

Though the personnel department of the company did not locate the mistake in respect of mismatch of your name or it may be it could be their ignorance. However if no corrective steps are taken up from your end, you would end up with a lots of financial loss by way of not getting your money due to you because of such an error.
In all respects, your name must be identical in all your academic certificates including Aadhar Card, PAN Card, Bank Account etc.
you will have to write an application to the personnel department of your company highlighting this anomaly to them and seek their advice on the corrective steps. They may advise you to get the anomalies corrected through the affidavit. Take the consultation of a lawyer to get the same corrected. He will do all your formalities for the affidavit and once this formality is over. Get the same published in two newspapers one of local language and the other one in a leading newspaper for its wide circulation. Submit the photocopy of the affidavit to your personnel department for the corrections needed to be done in their records.

This problem is faced by many people working in PSUs or any other such organisations where at the time of appointment itself some mistake in name or other data happens and then that remains in the records for a long time and then one fine day the person observes it and feels disturbed thinking about its consequences.
In such cases one has to follow some procedure to correct it back to the the correct name or anything like that.
Every organisation has a database of the details of the employees where all the details are available and many actions are taken based on that database only. For example the monthly salary is generally made based on that database only. The database also gets modified time to time depending on the number of employees leaving the organisation after reaching the stipulated date of retirement or resigning to go to other organisations or new employee joining the organisation etc.
The HR department takes care of all such database management and tries to keep the records up-to-date and correct. When any such mistake comes to their notice then they will process it and after obtaining the necessary approval from the authority incorporate it in their database. You have to bring this in their knowledge and submit the application or performa in the prescribed format and they will correct your name in their records. You have to present all your original certificates in support of your claim.
It is true that at the time of your appointment or later there was some mistake done in entering your records in the system. So it can be corrected now to avoid any inconvenience at a later stage.