I am writing a HTML formatted email notification rather than using the "OOTB" Notification. Do I need to have the condition below to check the "Process is Completed" and "Notify Owner" in my logic ? If any one has a logic the below screen, please do let me know.
Arun, the approach you undertaking using the 'Notifications' section, will just send the OOTB notification 'Process - Completed process step'. You do have the ability to modify this Notification but it will apply to all Processes using it. Note this will be a PPM notification, and unless the users have configured their notifications to include email, they may not receive the email.
If you want to send a custom email when the process has been completed, you need to add a new Action Item to the Finish Step, and include a 'Custom Script' - aka GEL script. See PPM: How to send email by using GEL script? - CA Knowledge as to the format.
If you don't have experience with Gel script, you could send an Manual Action (aka 'Action Item') as part of the Finish Step. If the users have email notification turned on for Action Items, they will receive the email.