If by "fast access squares" you mean the Speed Dial items, then you should probably just right click the item you want to edit and then select the Edit option in the list. This will give you the option to change the name of the item and also the web address. You can't add a custom logo, and, to be honest, I don't know how many people would use a feature like that. I wouldn't. The browser automatically fetches the site's logo from its server. You don't need to add it manually.
Also, it's always good to specify which version of Opera are you using. It helps quite a lot.