You cannot just change the name of the company at will; you have to apply to the Registrar of Companies and get the registration certificate amended. Additionally, you must take steps to update the service tax number, PAN number, TAN number, and all other legally registered documents. Don't forget to issue a notification in the gazette.
No changes need to be made to the documents given to employees, but from the date the company name is changed, you should issue all payslips and letters under the new name, with the old name in brackets. For example: SWEETY CO LTD (Formerly TWEETY CO LTD).
Next, you need to print new signboards, banners, and arrange for stationery accordingly. I have experience with this as we changed our organization's name last year due to some management changes, so I am familiar with the process.
Take care.