See the first section of the docs here:
http://www.concrete5.org/marketplace/themes/slate/documentation/...

Thanks Chris, but I can not change it. There must be a simple way?

So how to get rid of this "concrete5-website" text? I tried it via systems and settings > site name but nothing happend. What am I doing wrong?

It's in the docs that I posted the link to. Go to Dashboard->Stacks & Blocks and edit the Site Name stack.

Thanks again Chris!

Please see the attachments. I think I have followed your steps. But I do not see a 'site name stack'. What am i doing wrong?

Takes me loads of time to get rid of this 'concrete5-website' text. There is no "site name stack" under stacks as you can see. So I can not change it.

Also changing site name under "systems and setting" doesn't change the text on the website at all even after clearing cash.

Also editing header.php file is not possible. I am getting a bit desparate. Isn't there a simple way??

Ok, simply add a new stack called Site Name, then add a content block or image block and add whatever you want in there.