When you start a new Cocoon, you will be asked to name it on the first screen. Your Cocoon's name should be something that makes sense for the group of people you're going to invite. If it's your family, maybe something like Cornell Family, or Happy Family. If it's a group of friends, maybe something like SF Peeps, or Cool Cats. Don't worry, you can always change it later!
If you'd like to change your Cocoon's name, after you've completed the setup process, you can tap on the name in the header to edit it. See below.
Once you've tapped on the name of your Cocoon, an Edit dialog will appear where you can write a new name for the Cocoon. When you are finished, press Done.