With reference to below assumption, Our advise follows
e.g From XYZ Pvt. Ltd., to ABC Pvt. Ltd.,
Tradename has been changed... it means you will have to apply for new trademark regsitration ( it is a new trade name )
Ofcourse, domain name has to be changed... you can use the same website link... may be you can use the same web address & route it to new domain name.
Patents & Designs - An application can be filed to get the details changed of your company.
Feel free to contact me, if you need further details.
IP & Business Lawyer
IP Lex Global Services
Mob: 0091-09902007635 / 34