It depends on your employment agreement, if they allow you to do so. Technically your PAN remains same and unique unless you are registering with someone who lse name (brother, mother, father, etc.). Your company will have different PAN number though after registration.

A salaried person can start a private limited company or One-person company in India. However, the employment agreement of the salaried person must allow the person to start the company simultaneously. Generally, Employment contracts do not restrict to carry on a non-competing business.

The Companies Act, 2013 does not restrict the salaried employee to start a private limited

If you are a salaried person and pondering to start a private limited company, then you must read the internal employment guidelines first. If it allows, then contact the Professionals Team for complete guidance on how to start a company and what shall be the requirements.

you cannot carry on any business while being in employment of MNC 

2) it is ground for your dismissal 

3) start the business in your mother name or father name 

1) if you are in same filed of business your clients may inform the MNC 

2) your colleagues may inform the management 

3) if you advertise your products any inquiry by MNC would reveal you are the owner 

The question is not that how will your employer come to know about your this activity which is against the company's policy.

It is your problem that how you hide the details of your OPC from your employer.

We can give opinion about the legalities involved in your situation, rest of the things are to be taken care by you.

- There is no provision in Labour Laws , that an employee working in a private company cannot do separate business , like a government employee cannot enter into dual employment, i.e. cannot do financial, gain from another source, unless he is authorized in writing by the concerned department. 

-  Hence, you are bound to follow the restriction &rules, which you have signed at the time of joining your position in the company. 

- Since, there is restriction mentioned in your offer letter , then you cannot carry on said OPC without getting the approval of the company. 

- Even there is new PAN card , then also company may know the reality , and in that eventuality you will have to face the consequences for the non-compliance of the terms of the contract. 

Dear client,

If you operate a side business while you are employed, you may be in violation of your employment contract and face termination. Companies may find out about external business operations through a variety of channels, including social media, industry databases, or third-party reporting, even if they have a distinct PAN, bank account, and unaltered UAN. If you are set on moving forward, it is important to evaluate the dangers involved by carefully going over your employment contract, company policy, and local laws. Recall that in business dealings, openness is essential. Hide such activities from others could damage your reputation and put your job at risk. If you decide to pursue the OPC, think about talking to your job about your intentions, getting their approval, or looking at alternatives like getting a no-objection certificate to run your business concurrently.

Hope this helps you.