The real definition of diksha is, the process of getting pure divyam jnanam which destroys sins (di and khsha).
However, in the 1970s many of the people who got the formal initiation (diksha) ceremony and spiritual name from Srila Prabhupada, quite evidently did not really or fully accept the actual process of absorbing the divyam jnanam HDG was giving, so they fell from the path. Whereas we now have many new people who often never got any formal diksha ceremonials, but they are accepting the diksha process of getting the divyam jnanam from the pure devotee and his vani. Therefore the initiation process is primarily a matter of the aspirant accepting the guru and his orders (the guru vani process). The diksha ceremony is supposed to support and augment that relationship, but its not a guarantee of that relationship holding over time.
In short, the ceremonials are meant to aid that relationship, just like a marriage ceremony. The marriage ceremony might help the couple stay loyal to one another, .... but there is no guarantee that the ceremony will make the parties involved loyal. Its a formal declaration of loyalty, but the persons involved still have to endeavor to keep the bond together. And in our case: the disciple has to keep his end of the bargain. Sometimes we see that a marriage ends in divorce even a few weeks after the marriage ceremonials. So the ceremony alone, while it is an aid to assist the relationship, it is by no means a guarantee of the relationship.
The same thing has happened in the Gaudiya Matha, many formal initiates never really understood and accepted the process of divyam jnanam and they began concocting things, thinking they had a superior ideas to the acharya. They were not loyal to their guru, so their marriage to their guru was nullified by deviation. They had a divorce.
Its not just the ceremony where one gets a spiritual name, rather the ceremony is meant to give person a formal acceptance into the process of diksha, of accepting the guru's vani, just like marriage is a formal acceptance of the holy bond or marriage. Hopefully the aspirant will (again hopefully) take to the path of accepting the orders of the guru (the diksha path) seriously. The idea of the marriage ceremony is to convince the parties to remain faithful for their whole lives, that is the actual intent of the ceremony.
So Srila Prabhupada gave people spiritual names and that ceremonial "marriage to the guru" process should have continued via the ritvik priests. The true process of diksha is, that one is loyal to the guru and thereby, the guru is loyal to the aspirant. This is also true of our entire relationship with Krishna, if we take Krishna seriously, then He will take us seriously. He reciprocates according to the desires of the aspirant.
So the process of getting the divyam jnanam is mainly one of the heart of the aspirant. If one is serious, then the guru and Krishna will reciprocate accordingly. Therefore we have the phenomena of many of our new people understanding the divyam jnanam way better than those who got the official ceremony 40 years ago. These new people have more sincere hearts, so Krishna is giving them the inspiration to get the proper divyam jnanam. Whereas, people who have closed their hearts due to mundane desires overtaking the spiritual desires, the cannot penetrate into the divyam jnanam. Its actually not that hard to understand -- if we compare this to a marriage ceremony, the marriage may stay together, and hopefully it will, and the bond may increase over time, but beware, the bond may be dropped and end up in divorce.
Hope this helps, ys pd