The earliest mention of Brigham Young we have found...

Item # 685098

July 22, 1843

NILES' NATIONAL REGISTER, Baltimore, July 22, 1843

* Mormons - Mormonism
* Earliest of Brigham Young

The back page has a heading: "The Mormon Prophet" which begins: "The arrest of Joe Smith it appears was in virtue of some new process from Missouri. James Reynolds proceeded to Nauvoo to arrest him, found him absent..." with much more.
Further on is: "...The whole party made some stop at Nauvoo, where the Missouri agent says he was forced to go against his will...".
There is also a report from the Nauvoo Times & Season: "...published at the headquarters of Mormonism, contains the following special edict..." which calls the Mormons in Philadelphia to move to Nauvoo "...where God has a work for them to accomplish..." signed in type by: Brigham Young, President of the Quorum.
This is the earliest we have seen the name Brigham Young in a periodical, appearing two years before he would replace Joseph Smith as leader of the church.
Additionally, page 7 has: "Smith, The Mormon" which reports that: "Joe Smith, the Mormon Prophet, has reached Nauvoo in safely and has instituted suites against the persons from Missouri who arrested him...this new movement against Joe Smith grew out for disclosures made by Rockwell, in regard to the attempted assassination of Gov. Boggs...which led to the expulsion of the Mormons from Missouri and which were signalized by a savage and brutal vindictiveness on the part of a portion of our citizens..." with much more.
Four pages, 8 1/2 by 12 inches, very nice condition.