The question here is whether the first vowel in this name is an o or an e. In other words, is the name Boaz or Beaz ? In the printer’s manuscript, scribe 2 initially wrote Beaz; then he corrected the vowel to what looks like an o. The 1830 compositor, on the other hand, set Beaz. Quite clearly, the original manuscript reading must have looked something like Beaz.
Under Mormon 2:4, in the discussion regarding the name Angolah /Angelah, I observed that Oliver Cowdery frequently wrote an e-like o. This tendency on his part suggests that in the original manuscript for Mormon 4:20, Oliver (the presumed scribe here in 𝓞) accidentally wrote Boaz with an e-like o, which led both scribe 2 of 𝓟 (at least initially) and the 1830 compositor to transmit the name as Beaz. The 1837 editing to Boaz indicates that Joseph Smith or other editors for that edition realized that Beaz was a mistake for the biblical name Boaz (the second husband of Ruth as well as the name of one of the pillars in Solomon’s temple).
Scribe 2 of 𝓟 occasionally had difficulty writing the e vowel. Under Mormon 2:4, for instance, I list a number of names where scribe 2 wrote an e in place of the correct o. In addition, there are several instances here in Mormon where scribe 2 initially wrote the correct e vowel but then overwrote it to make it look more e-like; in these cases, his overwritten vowel looks more like an o, even when the context clearly requires an e:
The apparent motivation for these corrected e’s is that scribe 2’s original e’s often looked more like undotted i ’s, so by making a more expansive e, scribe 2 hoped to ensure the e reading, but the result was that his corrected e ’s often look like o’s! This does not cause a problem with doeth, neither, and leaders, but it does lead to possible misinterpretation with names. In other words, it is possible that scribe 2’s rewriting of Beaz to Boaz /Beaz in 𝓟 was simply an attempt to make the e more clear!
Ultimately, the 1837 decision to interpret the name here in Mormon 4:20 as Boaz, a biblical name, was probably correct, although we cannot be fully confident of this decision. In any event, the critical text will accept Boaz. For another example of the same difficulty with another name that is probably biblical, see under Mormon 6:14 regarding the name Shem.
Summary: The name of the city in Mormon 4:20 is probably the biblical name Boaz; Oliver Cowdery apparently wrote the name in the original manuscript so that the o looked more like an e.