The information you put in the 'Display Name' field of your group settings will eventually appear on the certificate in place of the [group.course_name] attribute. This will need to denote the achievement your recipient has gained and be easily recognizable.
In the event that you have two groups that need to have the same display name, you will need to have something to differentiate between the two groups. This is why there is also an 'Identifier' field in group settings. The information you place in this field won't appear on the certificate. Give your group a unique identifier so that you are able to find it easily in the Group Overview without mistaking it for another group with the same display name.
If you don't have many groups and there is a low risk of getting mixed up between them, you can keep things simple and make your identifier the same as your display name.