Can I transfer my profile gaming from one profile to a new one?

If you've forgotten your PSN password as well as the password for the associated email account that would be used for PSN password recovery, your only option is to contact Sony's customer service and explain your situation. They'll ask you to verify some of the other info on your profile such as date of birth just to make sure that you are indeed the account owner. After they confirm who you are, they can make whatever changes are needed or reset your password.

If you go to Playstation's Password Reset Help page, the very first question it asks is if you know the email. When you select 'no' and click 'next', it gives you a button to launch their customer service live chat and also shows you what their daily hours of operation are.