Wiccans often, but not always, work together in small, intimate groups of like-minded individuals. This group is usually called a Coven. You could think of a Coven as being part Spiritual Study Group, part congregation, and part social support.
Many people find that a Coven is the ideal way to practice the Craft, but unfortunately there are not enough Covens to go around. A Coven needs to be very small and intimate in order to balance the energies of the group (usually 3-13 people). A Coven can often be closer than family, because they share in so many deep emotional and spiritual experiences.
Like a family, petty disputes can tear them apart, so a Coven needs to be very careful in how they select new members. Everyone in the group must be able to work well with each other, and be able to trust one another explicitly. It can take a long time to find the right Coven, and an even longer time to join.
Because of the difficulty in finding an appropriate group to work with, many people practice solitary (either by choice or by necessity). I think it's important for everyone to practice their beliefs solitary for at least a year, before they join any kind of group. You need that long to decide for yourself what path you are walking, without undue influence from anyone outside yourself.
A Coven name is simply a name that a group gives themselves to give the group an identity. Individuals in a Coven might also choose a “magickal name”, which is a name with special, spiritual significance. Many times these magickal names are shared only with other members of the Coven.
~Flame RavenHawk