How to remove "Written by Admin" section on each post

Try adding the following code to either the bottom of the style.css file in your child theme, or if you don’t use a child theme and prefer not to create one, then add the code using a custom css plugin (Take a backup of any files before you edit them).

.post-author_h {
   display: none;
}

.post-author_gravatar img {
   display: none;
}

.post-author_link p {
   display: none;
}

Also, think about your security, as most site attacks are based on the username admin, with attempts to crack your password. Best bet is to create a new username in the WordPress dashboard with administrator rights (along with a nickname too), delete the admin username and assign all your existing posts to the new new user.