In Traditional Wicca one goes through an initiation ceremony conducted by your High Priest, High Priestess, and your other coven members before one is acknowleged as "Witch" and permitted to attend coven rituals. Initiation of course requires someone else to initiate you into a particular Tradition.
For solitary Wiccans and Witches there is no requirement that one undergo any sort of ceremony to make you a Witch. All that takes is to decide that is what you want to be and then do the hard work and study to learn all you can about your new path. And of course, one then needs to live that path every day.
Some solitaries decide to spend some considerable time in study (A year and a day is traditional) before committing themselves to the path of Wicca or Witchcraft. At the end of that time, or at any time you wish, you could perform a solitary dedication ritual to show your dedication to your new path. But such rituals are not mandatory at all, it's up to the individual whether they want to do them.
You might also want to understand that Wicca and Witchcraft are not the same thing.
Wicca is a modern religion begun in the 1940's and loosely based on the pre-Christian beliefs of Europe, ceremonial magic, Masonic rituals, etc. It involves very specific beliefs and practices. Wicca is a polytheistic relgion acknowledging many different Deities but generally honoring a Moon Goddess and a Horned God. While Wiccans do practice witchcraft and can therefore be called witches that is not the core of what Wicca is about.
Witchcraft on the other hand is a form of magical practice that can be performed by someone of any religion, or of no religion at all. Some Witches also integrate their magical practices into a generally individualized Pagan religion. But not all feel the need to mix religion and magic together.
So it would be accurate to say that "All Wiccans are Witches, but not all Witches are Wiccan."