Sir,
For change of name of company/factory, you can send the intimation to the appropriate Sub/Regional Office of ESIC as well as Branch Office Manager and Social Security Officer of your area intimating about new name and principal employers of the company/firm as well as the date of such change. The said Sub/Regional Office is expected to note the same in their record and send you confirmation also.
However, the liability of arrears/dues, if any, will be on both i.e.old as well as on new company as well as principal employers of the same. Kindly see Section 93A of Employees' State Insurance Act, 1948.