To be Initiated is to be reborn, in your own tradition, from one recognizable Life Stage into a new one. Initiations come regularly, as part of growth and decay inherent in Life's cycles, they can be noticed, studied, celebrated, mourned, felt, or ignored.
One leaves the Old Self behind when one is "Born into the Light" (in whatever initiation experience or tradition). To commemorate this transition, a new NAME is often chosen or bestowed, indicating a new beginning.
In the Bible, God has Adam NAME all the animals to establish dominion. Avram becomes Abraham (the YOD Stage of development) after his Initiation at God's hand. Isaac's initiation experience, the Binding of Isaac, is thrust upon him, not chosen, and he has no initiation, no NAME change, but remains rooted in the Land (the 1st HEH stage), Jacob travels, experiences his awakening at Beth El, and after wrestling with the Angel, is renamed Israel (Vau stage), and his son Joseph brings the Tribe to fruitful plenty in the foreign land of Goshen (final HEH).
Many traditions have tribal birth names, or new NAMEs adopted upon completion of religious or maturity rites. Marriage is another Life Cycle Event in which Names are often changed to indicate a shared identity. Divorce, as well.
However, the key component to it's success is in how well the ceremony instills a desire to UNDERSTAND the symbols now so dear to his or her point of view.* This should be nurtured by wise questions and encouragement, occasional warnings of pitfalls, and the understanding each must come to their own Wisdom, through the WORK, in their own Way, and producing a different "fruit".
All initiations introduce the Candidate to the Mysteries through symbols, which are not understood but have a visceral impact. By breaking down the old conception, the "bricks" and location inside us can be rebuilt along more perfect lines.
In terms of symbols, ceremonies and "content", the choice between well established traditions (Freemasonry, the Golden Dawn, OTO, & Gardnerian Wicca), or Creativity (as practiced in The Star Lodge and Oroboros Isis Gnosis) would be a first concern. The former have History and a degree of Authority, a set procedure to which each Candidate conforms. And if those Candidates need different things, they sort that out later, after joining the "Group" mind. Completely Individualized Initiations are tailored to the Candidate's needs and strengths, often combining elements of Traditional Initiations. However, they can be unbalanced because what the Candidate really needs is to become a Balanced, fully actualized Human Being eventually, not just cope with an obvious, current problem in their life.
Luckily, there is no need to choose, as one can be initiated into several Traditions, as well as create various personalized ceremonies for different stages of your own development. As your Path is completely unique, your needs will be as well, and some individual adjustments will prove useful.
Rather than discuss any specifics per se, either of Traditional or Personalized Initiations, what is the PROCESS by which Initiation causes Change, and what might be the RESULTS?
The Candidate must feel secure enough to give up personal control and have the experience of confusion and anxiety, secure in the knowledge they are being cared for by Friends or Brothers and Sisters.
To walk between the Worlds and experience the Divine, many traditions emphasis "In-Between-Ness", so the Candidate is neither barefoot nor shod, (one shoe on to walk the Earth, one foot bare to walk Sacred ground). Some emphasize the Initiation experience as a Rebirth, and have the Candidate naked as a baby, others continue the "In-Between-Ness" with the Candidate being neither Naked nor Clothed (ceremonial parts of the body bare, others covered) and still a third approach is the wearing of special clothing, like Robes.
Some traditions include such dichotomies as Naked / Bound, Pleasure / Pain, Meditation / Action in their "In-Between-Ness" experiences.
Blindfolding is the easiest way to lift us out of our normal wake-a-day world, as we are so dependent on sight to reassure us. Loud noises or knocks from different directions redirect the Senses to the Ears, Incenses or Oils to the Nose. While being lead by a Trusted Guide, all these things bring about the preconditions for Change. The Normal world is disrupted, and with it in flux, Change may take place. Without a real disruption of the normal consciousness, there is no space nor raw material for the proposed Rebirth.
Once the disruption of Normal consciousness is achieved by disorientation, a shock or surprise opens the Old Consciousness to new input, and the Lesson(s) of this particular Initiation are presented, usually as symbolic and powerful allegory. This is the language of Yesod, the Treasure House of Images, and "sticks" to the evolving Consciousness better than rational and complex information. That follows, after the Initiation experience, when the newly Born Initiate is given supplemental information and tasks, to learn by seeing, reading, listening and doing to reinforce the initial experience. Failure to follow-up will allow the habitual way of experiencing the World to creep back in, limited the usefulness of the entire experience.
Within the Initiation process, many of us believe receiving the Touch, the Blooodline, the Barakas, of Initiation requires that those who accept Initiation also accept the responsibility to pass on that energy to another before Death. This completes the circuit begun when we received a hand up in our Journey, and passes on the ancient covenant. But it has to be requested, not offered, to be legitimate.
The peek experience of Initiation fades, like all experiences, over time. It can be renewed, or supplemented, or its lessons may become the basis of your Life's WORK. If it has had the desired effect, you should experience the World, inner and outer, somewhat differently. Hopefully you will have built new skills to handle Life's challenges. Perhaps it reveals our current strengths and weaknesses, allowing creative application of the former to the latter. But above all, it should lead to increased flexibility once the Mono-Material-Mind has been cracked and the New You emerges. A noted side effect is laughter, as the Gravity of Life is best balanced with Levity.
FOOTNOTE: * This is where modern Freemasonry in America at least drops the ball. After amazing rituals of initiation filled with symbolism and puzzles, instead of directed questions leading the Entered Apprentice and Fellowcraft to an understanding of their experience, they are met with the demands of rote memorization. Memory IS very important, but it should be the preliminary step in self understanding through the symbolism of the Lodge and ritual. But the directed discussion is usually lacking in most Lodges, and the Scottish Rite in the North at least is substituting morality plays (once again, not a bad thing in themselves) for the Ancient Wisdom designed to make one think.