“Then the white stone mentioned in [Revelation 1:12] will become a Urim and Thummim to each individual who receives one, whereby things pertaining to a higher order of kingdoms will be made known. And a white stone is given to each of those who come into the Celestial Kingdom, whereon is a new name written, which no man knoweth save he that receiveth it. The new name is the key word.”1 Since the white stone and new name mentioned in it are referring to the state of exaltation and inheritance, and since the promise which the Second Comforter (Christ) is working to obtain for those to whom He ministers is the promise of exaltation, that equivalency may also be made. The difference is that those described in this statement are in a future state in which they have actually inherited the condition of exaltation, have entered into the Celestial Kingdom to dwell there, and possess the white stone on which their new name is written; whereas the promises Joseph speaks of in reference to the Second Comforter2 and the promises in T&C 86:1 are given to a mortal and are to be realized fully in the future.3
1 D&C 130:10–11. Section 130 of the LDS Doctrine and Covenants first appeared as canon in the 1876 edition prepared by Orson Pratt under the direction of Brigham Young. For the original source from the Journal of William Clayton, see JSP, Journals Vol. 2:404, Appendix 2, 1–4 April 1843; WJS, 169, 171, 267n4.
2 See WJS, 5; 17n1; JS, Discourse, Commerce, IL, between 26 June and 2 July 1839; in Willard Richards Pocket Companion, pp. 19–21; handwriting of Willard Richards; Willard Richards, Journals, CHL, JSP, https : //www.josephsmithpapers.org/paper-summary/discourse-between-circa-26-june-and-circa-2-july-1839-as-reported-by-willard-richards/3.
3 “White stone and a New Name,” March 23, 2010, blog post.