There are numerous examples of the ways Ayn Rand shows the society in Anthem as taking away each person's individuality. Early in the novel, Equality refers to one of his sins: the Transgression of Preference. Citizens of that society were taught that it was an egregious wrong-doing to prefer one anything over the other. This pertains to all facets of life including friends and careers. Even having a preference concerning a partner is discouraged, and the Council instead uses the House of Mating. Babies and children are not allowed to stay with parents to prevent any differences in upbringing that might set someone apart.
One of the most predominate ideas that pertains to destroying individuality, however, is the naming of the citizens. Using a number strips a person of who he or she is at the core. That is why it is so powerful for Equality when he names himself Prometheus.
In the above ways and more, the society in Anthem effectively strips each person of his or her personal choice, desires, and values.