How to prevent users from seeing their own notifications on my website?

Go to notification list > edit notification > Data & Timing tab >click on  notification data setting

Often a user sees the data of his action on the website. You can make the arrangement in the advanced option so that visitor who submits the form cannot see their own activities in the notification.

Here you will find an option called ‘Skip own data in notification’. make sure you turn it on. After that, if any visitor submits the form, he/she won't see their own activities in the notification.