Jerry D. Grover, Jr., proposes various Hebrew and Sumerian etymologies for the personal and place name "Josh" in the Book of Mormon.
Jerry D. Grover, Jr., Sumerian Roots of Jaredite Derived Names and Terminology in the Book of Mormon (Provo, UT: Challex Scientific Publishing, 2017), 246-47
The Book of Mormon Personal Name and Geographic Name JOSH may be a hypocoristic form of the Hebrew biblical PN Josiah (Zechariah 6:10, yoʾšiyyȃ, and Jeremiah 27:1, yoʾšiyyȃhû), that is, Josiah minus the theophoric element. Meaning Josiah, and therefore JOSH, could mean “Jehovah has healed,” from the hypothetical HEBREW root *ʾšȃ, “to heal,” posited on the basis of the attested Arabic root ʾsā, “to heal.” On the other hand, Josiah, and thus JOSH, could mean “Jehovah has given,” or “gift of Jehovah,” from the West Semitic root ʾwš, “to give a present” (see Ugaritic ušn, “gift”). As such, JOSH may be related to the biblical period HEBREW PN yʾwš, attested in the Lachish ostraca (where it probably had the pronunciation yāʾuš) and in the Elephantine Aramaic documents. In either case, the Nephite form JOSH, if it does derive from ʾwš or ʾsā, suggests that the aleph must have become quiescent by the time the name appears in the NEPHITE record.
Probably unrelated are the instances of the Amorite names containing ya-(ú-)uš plus a theophoric element, etc., listed in Huffmon, Amorite Personal Names in the Mari Texts (Balimore: Johns Hopkins, 1965), 171. Not only does Huffmon list the root as “uncertain,” but he suggests the preferred etymology be taken from *ġwṯ. JOSH as a hypocoristicon of Jeshua is somewhat less likely. Ancient Semitic hypocoristica do not function in this manner, i.e., whole lexemes can be dropped, but the lexemes themselves are not subject to being split apart or syncopated. Therefore, JOSH, contrary to the origin of the modern nickname, is not an ancient hypocoristic form of Joshua (from the HEBREW root yehoshua), where Jo- is a shortened version of Jehovah and –shua is from the lexeme for “help; succor.”
Less likely is a derivation from the HEBREW existential particle, yēš, “there is.” It would be hard to account for the /o/ in JOSH from the /ē/ in yēš.
(Book of Mormon Onomasticon 2016)
Josh is the name of a Nephite military leader slain in the final battles with the Lamanites along with his “ten thousand” (Mormon 6:14).
Reasonable etymological units for Josh are:
Sumerian
a: arm; strength; wage; power
a2-še3 (form of a)
u: admiration
u6-še3, (form of u)
u: defeat
u: ten
uš: to die; to be dead; death
Constructed Compound Word: Josh
Hebrew
ya'ash: to despair
'ish: man
A city of Josh was a wicked city identified as part of the destruction that occurred at the death of Christ. The city was destroyed by being burned with fire, with the fire being sent down (3 Nephi 9:10-11). The description is referencing fire caused by fallout or pyroclastic flows from a volcanic eruption (Grover 2014), and it was indicated that the wickedness of the city was of casting out prophets and stoning them.
Reasonable etymological units for the city of Josh are:
Sumerian
a'aš: curse
ah: (to be) dried (out), dry; to dry
ah3-še3 (form of ah)
ah: a paste (interpreted as volcanic material)
ah3-še3 (form of ah)
aš: curse
uh: trachea, uvula (interpreted as a volcanic
vent)
uh: to make paste
uš: to shut off, block up
uš: blood, gore
uš: to die; to be dead; death
Constructed Compound Word: Josh
Hebrew
'esh: fire