Company name change procedure regards

Complete Procedure for Name Change of pvt Ltd
1. Pass a Board Resolution for name change.
2. Check the availability from Trademark registry @ ipindiaonline.gov.in then apply in RUN service.
3. Hold an EGM and pass a Special Resolution for name change and alteration in MOA & AOA.
4. File MGT-14 and INC-24 along with prescribed fees.
5. Obtain new Certificate of Incorporation.
6. Incorporate the necessary changes to MOA & AOA

Thank you for this...
There is some gap in days of the day name change happens and the day it changes in Bank account/ Cheque book. Is there a way or any act which can help us make clients understand to make payment in old account?
Please note Invoice is raised as per new account name and bank account is old.