"SL. Clemens," or "S.L. Clemens," is probably the way MT most often signed himself, though I don't think anyone else called him that. Here MT uses it to sign a letter to President-elect James Garfield in which he recommends that Garfield keep the noted African American Frederick Douglass (note that MT misspells the name) in his position as Marshal of the District of Columbia (a politically appointed job).
MT and Douglass first met in 1869. They were two of the most famous Americans of their times, both highly regarded as speakers, but became acquainted mainly through Douglass' long-standing relationship with MT's in-laws, the Langdons, active abolitionists before the Civil War (MT mentions his brother "on my wife's side" in the letter). Douglass wrote MT on 22 January 1881 to thank him for the recommendation. Garfield, however, gave the job to someone else.TRANSCRIPT OF LETTER