There have been a number of questions about acquiring a Craft-name, or, as it is also commonly called a ‘Wiccan name’.
There are three basic kinds of Craft-names. There is the one one uses publicly; at public gatherings; online; etc. Then there is the Craft-name your coven gives you, which is traditionally kept secret and used only among coven members. The third is the most sacred. It is the name that is only known to yourself and the Goddess and the God. It is your true name and it is the name you would use in private, personal rituals. Not all people chose to have all three, some use one or two, or even none but your given name. It’s a matter of personal preference.
The public name you choose can be anything you like that comes to your fancy. Often people incorporate the elements into their name. Trees, flowers, herbs and other plants are also quite common; as are totem animals.
The same type of thing might be used for a coven Craft-name, but it is kept private, and usually only used inside the coven circle. In some covens the High Priestess will give an initiate a Craft-name upon first degree initiation, and a new one for their second degree, and yet a third one for their third degree; as a way to mark their progress in the understanding of the Divine and magick. In some Traditions and/or covens the High Priestess will allow the initiate to choose the name, in others the initiate may choose the name, and have it approved by the High Priestess, and yet in others the High Priestess chooses, and the initiate has no say.
The private name you use only in communion with the Goddess and the God is the most sacred of names as it is the name the Goddess and the God give you. Sometimes it is revealed in a dream, other times it may come while you are awake, or perhaps during meditation, etc.
I hope this sheds a bit of light onto understanding Craft-names.