A plan nickname is just another name you can give each hosting plan you have with Slamdot. For instance, instead of using your domain name, xyzcompany.com, as your nickname, you could change the nickname to My Business Website. This is useful if you have a plan for, say, your personal website, too, which you could change from yourname.com to My Personal Website. It simply lets you be more descriptive with your plan names.
To change the nickname for a plan, go to your dashboard and click the change nickname link next to the appropriate plan. Enter the name you want to give it and click save.