May Cremated Remains be Kept at Home?

No. The (U.S.) Bishops’ Committee on Divine Worship says the following:

Any catechesis on the subject of cremation should emphasize that the cremated remains of a body should be treated with the same respect given to the corporeal remains of a human body. This includes the use of a worthy vessel to contain the ashes, the manner in which they are carried, the care and attention to appropriate placement and transport, and the final disposition.

While cremated remains may be buried in a grave, entombed in a mausoleum or columbarium or even buried at sea, the practice of scattering cremated remains on the sea, from the air, or on the ground, or keeping cremated remains in the home of a relative or friend of the deceased are not the reverent disposition that the Church requires. The cremated remains of the body may be properly buried at sea in the urn, coffin, or other container in which they have been carried to the place of committal. (“Cremation and Burial at Sea”)

See the USCCB on cremation.

Nota bene: In December 2023, the Discastery for the Doctrine of the Faith ruled that, provided local civil norms are observed, the Church can authorize a family to keep “a minimal part of the ashes of their relative in a place of significance for the history of the deceased person,” e.g., in the family home.