Answer
The first thing to understand is how the subconscious mind works.
The subconscious is constantly learning. Every experience, good or bad, is stored there. If you repeatedly reacted negatively to certain situations in the past, those reactions become programmed. Later, when similar situations arise, the subconscious automatically brings up those learned responses.
However, this programming is not permanent.
If, instead of reacting in the old way, you consciously respond differently, the subconscious gradually relearns. It is simply a learning mechanism. It repeats whatever you have taught it.
Understanding this gives confidence. Just as the subconscious has learned impure habits, it can also learn pure devotional habits. It is simply a machine that stores experiential memories.
The holy name has the power to cleanse these old impressions and pleasure memories. Without the help of chanting, genuine transformation of perception is almost impossible. External events may temporarily alter a person's behavior, but they do not fundamentally transform one's personality.
Our hope is to purify our perception through sincere chanting of the holy name.
The same principle even applies to chanting itself. Previously, the mind had never learned to chant. Then we trained it to chant while simultaneously thinking about many other things. Now, if we consistently practice chanting while simply hearing the holy name, the mind can learn that too.
The subconscious learns whatever we repeatedly teach it.