That makes sense.
If you want to change every classname of every plugin:
AFAIK, there's no tool to actually do that.
You could, in theory, change the class names from the source code, but it will likely take a lot of time until you get it right, and it will be gone once the plugin updates.
Changing classes dynamically, while WordPress is generating the html, is definitely going to impact perfomance and SEO, besides not letting JS code know about the change.
So automating that process is the only way I can see.
To remove your template's information.
You can remove the headers from styles.css and any reference to your template's name you find in editable text.
Change the directory name (you can also do that with plugins, but it is probably useless).
And I saw some guys changing .htaccess to actually hide the folder of the plugins changing the base url.
And also you can do minification and mix every CSS in a single file, but we know that usually breaks a thing or two.
That's all I can say