There are several ways to make a club your own. (Most changes are done on your contact page)
When you first create your club you set the club name. Of course, you can always change the name again. Go to your contact page "Club -> Contact page" and click on the pen symbol next to your club name to change it.
Changing your club name costs you 25.000 €.
On the same page you can also set individual names for your supporter's club (free) and your stadium (25.000 €).
As a premium account holder, you can upload individual logo and choose shirt designs. Go to your contact page and open the tab "Logo and shirts"
You can set individual designs and colours for home and away matches.