Sometimes, people ask me to pray for them. I tell them that I will. From a religious point of view, these people might think that I kneel down and pray to a deity or bodhisattva to help them. Perhaps they think I have a hotline to the Buddha. I don't have any special connections, and I don't pray. Then why do I agree to pray for these people? Two reasons. First, if I say I will pray for them, they'll feel better. Usually, that's all people need. Second, I can transfer merit to these people through the power of my practice. People who practice can transfer merit to others. In fact, even without practice, people who are sincere in their intentions can bring about a good effect on others. The opposite is also true. If many people wish someone harm, then that person will likely suffer. It is not magical. It is merely the power of the mind.
I recite Avalokitesvara's name, with the idea that my merit will be transferred to others. I do not care if he exists or not. Why do I bother? First, Sakyamuni Buddha praised Avalokitesvara and his power, and I trust the Buddha's words. Second, precisely because so many people believe in and pray to Avalokitesvara, his power exists. For these reasons, I recite his name, and use him to transfer merit.