Even though it might have been a trend for the celebrities to use a phone in other's names, today it isn't a legal option. With the strict identity rules and regulations implemented in the telecom services, one has to make a chain of identity proofs to verify their identity as innocent citizens.
What is done to protect their privacy, is subscribing to the services of private number status specially done through the Telecom Regulatory Authority of India (TRAI).
The other way, is that, they never share their personal numbers to any online shopping site, or any website that can use or misuse their identity.
Today, as mobile has become a part of your identity proof, its security and privacy is also taken care by the concerned authorities of the Telecom Regulatory Authority of India (TRAI).
Hence, they always choose the security options carefully and never allows any information leaks to take place.
For online shopping and for other stuffs, where sharing phone number is compulsory, they might be using numbers of their close ones.