On both student profiles and in My Classroom there are a number of demographic indicators, or tags, that are automatically displayed so you're able to quickly gain a more holistic understanding of the student at a glance. You can see a full list of these here.
It isn't possible to create more Demographic groups. However, you can create new Custom Groups which you can select in reporting.
It isn't possible to add more further additional tags to this list. To flag important information on student profiles, you can either: