The act of abandoning one's religious faith is known as apostasy. The term is also used more generally to talk about leaving a cause or political party. As a general rule, someone does not self-identify as an apostate, as the term is considered to be rather pejorative.
The word is derived from a Greek term which means “to abandon one's post.” Many religions include a prohibition against apostasy, which is considered to be a serious sin. Someone who abandons God altogether may be termed an atheist as well as an apostate, but someone who converts to another religion is also considered an apostate. In either case, some religious faiths believe that apostates are doomed to eternal torment for abandoning the true faith.
In addition to the presumable punishments of hell suffered by apostates, apostasy has some very real earthly consequences as well. On the more mild end of the scale, children of an apostate may face rejection and difficulty if they attempt to carry on their faith or to marry into their church. On the more severe end of the spectrum, apostasy is considered a capital crime in some countries, especially fundamentalist Islamic nations.
In order to commit apostasy, someone must publicly and formally reject his or her faith. If someone chooses to stop attending religious services, praying, or observing religious practices, he or she may be considered lost, but not necessarily an apostate. An apostate makes a formal renunciation which signals a permanent break with the faith, and this breach cannot be repaired.
In many cases, the term is used pejoratively by people who remain within the faith. People may suggest that someone left the faith because they are weak, or for petty reasons. In most cases, an attempt to make an examples of the apostate's life and choices will be made, so that other members of the faith do not follow suit. This is especially true with cults and extremist sects, which do not want to encourage defection on the part of their members.
Choosing to commit apostasy can be very difficult, even when one is not threatened with death. The choice to publicly separate and potentially later criticize a religion is not taken lightly. Generally, someone must be very faithful to commit apostasy in the first place, since only a profound crisis of faith can lead to such an action. It can also be difficult for someone considering apostasy to find a good spiritual adviser, which can be very alienating.