While many religious communities did choose to modify their habit and many of these, with the approval of the church, eventually stopped wearing the traditional habit, others did indeed continue wearing habits. Some of these communities are active religious sisters and some are cloistered contemplative nuns.
Because each community is uniquely called by God, how they chooose to dress depends on their particular ministries, customs, and way of life. For some communities a recognizable uniform worn regularly (a habit) is not essential to their life and mission, while for others it is. A sister or nun can serve God fully and authentically in her prayer and ministry regardless of what she wears.
Taking a religious name is not a matter of whether or not one is a sister or a nun but rather of the customs of a particular community. Some communities of sisters and of nuns have the custom of using one’s baptismal name, and others the custom of taking a religious name.
The changes in customs that have taken place most noticeably since Vatican II were never made lightly but were the results of much prayer and discernment. Religious sisters and contemplative nuns are called first to faithfulness to God, even if that means that a much-loved custom no longer benefits that particular community’s God-given mission.