The question for this passage centers around whether there is an e or an o vowel in the first name listed here. In the printer’s manuscript, scribe 2 initially wrote Shem, then rewrote the e vowel, but his correction looks like an o. The 1830 edition reads Shem. Very likely 𝓞 read Shem.
It seems quite reasonable that the biblical name Shem is intended here in Mormon 6:14. For a similar case of a probable biblical name that involves the rewriting of e/o, see the discussion regarding the name Boaz under Mormon 4:20. Also see the discussion under Mormon 2:4 regarding the second vowel in the name Angolah.
There are quite a few biblical names in this part of the Book of Mormon text, in support of the decision to choose Shem here in Mormon 6:14 (and Boaz in Mormon 4:20). From 3 Nephi 19 through the end of Mormon, we have these additional names from the Bible: Timothy, Jonas, Jeremiah, Zedekiah, Isaiah, David, Joshua, Aaron, and Gilgal (all of these are used to refer to individuals or places that make their appearance only in this part of the text). In addition, the name Shem is used in Mormon 2:20–21 to refer to a land.
Summary: The name of the Nephite leader in Mormon 6:14 is most probably the biblical name Shem, not Shom.