Hi @re2arthouse!
You can completely remove items from the menu like this (these should be inside the init callback on your main.js)
monogatari.component ('quick-menu').removeButton ('Hide');
monogatari.component ('quick-menu').removeButton ('Log');
In the case of the Dialog Log, if you wish to get completely rid of it, I believe you can also just remove it from your index.html file and it will go away. You can see all the buttons that are added initially here.
To add your own buttons however, you would simply use other functions like the removeButton which you can see here: https://developers.monogatari.io/documentation/components/quick-menu