When teaching beginners, I usually ask them to count or follow the breath; if they have been using the hua-t'ou method for a long time and are doing well with it, I'll allow them to continue. If people are accustomed to reciting Amitabha Buddha's name, I'll let them continue but with certain modifications. In order for the practice to be a Ch'an method, practitioners may not recite the name with the desire to be reborn in the Pure Land.
As a Ch'an method, reciting the Buddha's name ─ or a mantra for that matter ─ is no different from counting the breath. Its purpose is to help calm the mind. When a reciter of the Buddha's name reaches a point where the mind is calm and concentrated, he or she can then start to ask, "Who is it that is reciting the Buddha's name?" In essence, the method has been turned into a hua-t'ou. I rarely instruct practitioners to start with a hua-t'ou, because if their minds are not calm, then the hua-t'ou will not help them to give rise to a sense of great doubt. Giving rise to a sense of great doubt is the purpose of the hua-t'ou. If it doesn't work, then the method is useless.
Some have said that if you turn reciting the Buddha's name into a hua-t'ou, it is simultaneously a Ch'an method and a Pure Land method. In reality, this is Ch'an practice.
In Ch'an, people may begin with the hua-t'ou method or by reciting Buddha's name. Practitioners of the Lin-chi sect may begin by counting breaths or by reciting the Buddha's name, but eventually they should progress to a hua-t'ou. Whereas in Rinzai Zen students are given one hua-t'ou after another, Lin-chi Ch'an students may work on the same hua-t'ou for their entire lives.
Practitioners of the Ts'ao-tung sect may begin to practice by counting breaths, or more likely, by reciting the Buddha's name. They will not, however, turn the method into a hua-t'ou. Instead, when the mind is calm, practitioners will practice silent illumination, which is very similar to shikantaza.