"The dead will be after you, they will seek after you as they have after us in St. George [temple]. They called upon us, knowing that we held the keys and power to redeem them. I will here say before closing, that two weeks before I left St. George, the spirits of the dead gathered around me, wanting to know why we did not redeem them." (Journal of Discourses, vol. 19, p. 229, Wilford Woodruff)."
Someone questioned the following quote from Wilford Woodruff who was the 4th Prophet and President of the Church of Jesus Christ of Latter-day Saints. This person was concerned that this quote advocated the forbidden practice of spiritism or divination. First off, this question is a reflection of an unfortunate misunderstanding of the quote. Pres. Woodruff is not speaking of the living seeking to communicate with the dead, but the dead trying to inspire the living.
Let me be clear from the start that the LDS Church strictly forbids its members from praying to anyone other than Heavenly Father in the name of Jesus Christ or from practicing any type of spiritism or seeking communication from anyone who has died. Any practices of this sort invites evil spirits who will deceive you.
I and many other LDS and non-LDS have been prompted to do genealogy and family history work. Not in the same way as Pres. Woodruff. But the unseen motivation to seek out our dead ancestors is real. This desire to do Genealogy work which is the spirit of Elijah is why so many people are interested in family history research. This spirit is in fulfillment of the prophecy in Malachi which says in the Last Days Elijah will appear and hearts of the fathers will turn to the children and the hearts of the children turn to their fathers.
Mal 4:6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
Luke 1:7 And he shall go before him in the spirit and power of Elias, to turn the hearts of the fathers to the children, and the disobedient to the wisdom of the just; to make ready a people prepared for the Lord.
Luke 1:17 is speaking of the mission of John the Baptist to baptize the living before the first coming of Christ while Mal 4:6 is speaking of Elijah himself coming before the great and dreadful day of the Lord to restore the keys of baptism for the dead before the Second Coming of Christ. Elijah appeared to Joseph Smith and restored the keys of this work in the Kirtland Temple on April 3, 1836. So, John the Baptist came in the spirit of Elijah to baptize the living before the First Coming of Jesus Christ and Elijah himself came to baptize the dead before the Second Coming of Jesus Christ.
Since names may be required to resurrect people and call them out of the Earth, it would be useful to do all the genealogy work so that the righteous can be resurrected during the Millennium. Christ could do it all himself. But that is not how he operates. He allows man to participate in this work just like He allows man to participate in the building up of His kingdom on Earth and in doing missionary work.