"The name of this organization shall be Socialist Labor Party". Art. I, Sec. 1 of the Constitution of the Socialist Labor Party of America adopted at the Eleventh National Convention (New York, July 1904; amended at the National Conventions 1908, 1912, 1916, 1920, 1924, 1928, 1932, 1936, 1940, 1944, 1948, 1952, 1956, 1960, 1964, 1968, 1972, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1987, 1989, 1991, 1993, 2001, 2005 and 2007) (cited February 18, 2016).
While the 1885 constitution and platform uses the term "socialistic" in the party name, the 1890 constitution and platform uses the term "socialist" in the party name. As both of these sources appear to be scans of original documents, it is safe to assume that this second name change necessarily occurred somewhere between 1885 and 1890. Unfortunately, the other sources provided by the SLP are not original scans and must be taken with a grain of salt. The Report of the Proceedings of the Sixth National Convention of the Socialistic Labor Party, Held at Buffalo, New York, September 17, 19, 20 & 21, 1887 (New York Labor News Company: New York, September 1887) would seem to indicate that party was still calling itself the Socialistic Labor Party in that year. While the majority of the .pdf is not an original scan, the cover page is. Yet, the 1887 platform (which is in no part an original scan) would seem to indicate that the party was calling itself the Socialist Labor Party by 1887. Likewise, the 1889 platform (reported in this non-scan copy of the Workmen's Advocate on October 26, 1889) employs the name Socialist Labor Party.