Question: If I wish to help someone having a hard time far away, will my mindfulness of the Buddha’s name (i.e. Āmítuófó’s: 阿弥陀佛) name be able to help?
Answer: If the intention is clear that you are connecting to the Buddha for blessings to help them, this generating of meritorious virtues (功德) will be dedicated (回向) to them directly.
According to the natural karmic law of dedication, one-seventh of the merits created will be dedicatable: https://thedailyenlightenment.com/2017/10/why-merits-can-only-be-partially-dedicated.
There is also a formal way to dedicate merits, by reciting the Dedication Verse (回向文) after reciting the Buddha’s name for some time: https://purelanders.com/2010/03/15/the-pureland-way-of-sharing-merits.
This is how to recite the Buddha’s name well: https://purelanders.com/start.
