This is the only place in the Book of Mormon where the name Shimnilom appears. According to the earliest textual source, the printer’s manuscript (the original manuscript is not extant for this part of the sentence), the name ends in m. The 1852 LDS edition accidentally replaced the final m with an n; the same error occurred in the 1953 RLDS edition. The 1920 LDS edition, following the earlier editions, restored the correct spelling, Shimnilom, to the LDS text.
The most likely source for the incorrect Shimnilon is the preceding name Shemlon (which ends in n), although before that we have the name Shilom, which supports the correct spelling ending in m. Interestingly, the name Shemlon was accidentally replaced with Shemlom in the 1841 British edition in Mosiah 10:7. (The correct Shemlon was restored in the subsequent LDS edition, in 1849; see the discussion under Mosiah 10:7.) For mix-ups regarding the names Shiblom and Shiblon, see the discussion under Ether 1:11–12.
Summary: Maintain in Alma 23:12 the name Shimnilom, the spelling found in the earliest textual sources.