Catholic last rites are three things, and the popular name has attached itself to the wrong one.
Anointing of the sick, until 1972 called extreme unction, is not reserved for the dying. It may be given to anyone seriously ill or facing surgery or weakened by age, and it may be repeated. The Second Vatican Council changed the name deliberately, because reserving it for the deathbed had turned its arrival into a verdict: families delayed calling the priest, in order not to tell the patient what everyone had concluded, and the sacrament arrived too late to be received consciously or not at all.
Confession precedes it where the person is able. And the last sacrament properly speaking is Viaticum, communion given to the dying, whose name means provision for a journey. That is the one that is actually last, and hardly anyone outside the church knows the word. An apostolic pardon, a plenary indulgence at the hour of death, may be added.
The Orthodox churches have their own sacrament of unction, administered to the sick generally and in some traditions to the whole congregation in Holy Week, which makes the deathbed association still weaker there.
The other traditions organise the deathbed around speech rather than around a rite.
In Muslim practice those present prompt the dying person gently toward the declaration of faith, so that it may be the last thing said, and the thirty-sixth chapter of the Qur'an is commonly recited at the bedside. Nobody administers anything.
Hindu custom places water from a sacred river and a leaf of holy basil in the mouth, and the family reads scripture aloud; dying at Varanasi, or with the Ganges within reach, is held to be worth arranging for.
Tibetan Buddhist practice is the most explicitly instructional. Texts are read to the dying and continue to be read to the newly dead over a period of days, on the understanding that consciousness persists, can still hear what is said to it, and faces a sequence of decisions in which guidance is useful. It is the one deathbed practice in this list that treats the person as still an agent rather than as a recipient.