I would just like some clarity on this.
Answer: Use of the term, “alter ego”, implies that someone has an alternative self, which is believed to be distinct from a person's normal self. A rose by any other name would still be a rose…and would still smell as sweet.
Nevertheless, I suppose that it could be honestly said that this practice is akin to the alter egos found among folks who do belong to the Society for Creative Anachronism (SCA).
For those who do not know, the SCA is an international living history group with the aim of recreation of and studying of pre 17th century skills, arts, combat, clothing, and culture. The SCA was founded May 1, 1966.
Nevertheless, Gerald B. Gardner (June 13, 1884 - February 12, 1964), author of Witchcraft Today, 1954, and now recognized as "the Father of Modern Witchcraft" was also known by the Wiccan name or craft name “Scire”. Futhernore, Doreen Valiente (January 4, 1922 - September 1, 1999) likewise recognized as the "Mother of Modern Witchcraft" or "Mother of Wicca", was likewise known by her Wiccan name or craft name “Ameth”.
In my experience, such names are now generally described as being either a “Pagan name” or a “Wiccan name”. However, I would not be surprised that the term “craft name” is still in use in some areas.
Wiccans do not prosyletize; we are not expected to spread the Good News of the Goddess. Thus, some people do indeed prefer to keep their practice private, "in the broom closet". Seriously, why talk to people who are already happy with whatever religion they have?
Personally, I think it is delightful to have another name—aka “nickname”—which is shared among certain friends. The word nickname is etymologically derived from “eke name”. The term, “eke name” dates back to the early 14th century, and literally it meant simply: “an additional name.”
Myth Woodling, January 2021