Answer
Chanting of the Divine Name (Nama Japa) can be undertaken with two purposes. The first is simply for one's own spiritual growth, for self-purification, and for drawing closer to God. The second is when Nama Japa is performed to obtain a specific result — such as the birth of a son, the cure of a disease, or the fulfillment of some particular desire.
If the chanting is being done for a specific outcome, then surely you must have taken a sankalpa (sacred resolve) — deciding how much chanting you will do. Someone must have guided you regarding how many days or how many repetitions are needed for the fulfillment of that desire.
In such a case, once the prescribed number is completed and the desired result is obtained, the japa has been successful; if not, it has not succeeded.
If your japa is done with nishkama bhava (selfless intention) — for your own purification, for deepening your closeness to God — then you yourself must assess how much purification has occurred within you, how much your devotion and love for God have grown.
Sometimes, even through selfless chanting, after some years certain siddhis (spiritual powers) begin to manifest. The same siddhi does not arise in everyone. For instance, if someone was in pain and you placed your hand upon them and chanted the Name briefly, the pain disappeared. Or knowledge of the future began to arise spontaneously. Sometimes, visions of God (darshana) also begin to occur.
A very great sign that one's Nama Japa has become successful is this: when you begin chanting the Lord's Name, tears repeatedly flow from your eyes. This is the proof — and a very great proof — of the success of your japa. It is a sign that the gates of Vaikuntha are about to open for you.
In the Ramakrishna Mission, during Ramakrishna's lifetime, there was a woman known as "Gopala's Mother." The Ramakrishna Mission has published two large volumes on Ramakrishna — one containing his teachings and the other his lilas (divine play). From my recollection, I read this in the second volume. She chanted the name of Lord Krishna continuously for thirty years. Her heart held vatsalya bhava (motherly love) toward Lord Krishna, which is why people called her Gopala's Mother. After thirty years, one day while she was chanting, Lord Krishna suddenly appeared in her lap. And He did not merely appear — He began crying loudly, demanding kheer (rice pudding), and troubling her. Carrying Him in her lap, she ran about trying to soothe Him. In the meantime, He also disappeared from sight.
Surely after that she must have continued to have divine visions of the Lord, though I did not immediately find further details in that book published by the Ramakrishna Mission. But the first darshana took thirty years.
Chant the Lord's Name with faith and trust, and do not worry about the result. If you chant not mechanically but with heartfelt devotion, and alongside that you engage in acts of benevolence, cultivate compassion in your heart, and free yourself from negative emotions, then you will certainly begin to have visions of the Lord. Those who chant the Name outwardly but inwardly harbor deceit — the proverbial 'Ram on the lips, a dagger under the arm' — they never receive darshana, even if they chant for fifty years.