Dear Karan
Its better to update Company's name in TDS record, for this, Co. has to fill a form "Changes or correction in TAN data" It is available on tin-nsdl.com. Also all the procedure are mention there, You could read that. While submitting the filled form supporting documents are to be attached.
Since its a company, RoC must have issued a fresh Certificate of incorporation, Co. could attached that or one can go to nsdl office/ alankit/tin facilitation centre where these forms are to be submitted to ask for proper documents to be attached as there will be no hassle while submitting the form
It is advisable to update the name in PAN Card also, for that a separate form "Changes or correction in PAN data" is available over same website along with other instructions.