In this post I will not address the problem with the NASB's choice to translate "head of thirty" both in v. 11 and v. 20, for this @ba has already provided an illuminating answer. My intention is only to provide what I think is the best and most accurate translation for v. 11 and v. 20, and I hope this will shed some light on this very confusing topic.
Jashobeam
V. 11 according to the Hebrew as preserved in the MT:
וְאֵלֶּה מִסְפַּר הַגִּבֹּרִים, אֲשֶׁר לְדָוִיד: יָשָׁבְעָם
בֶּן-חַכְמוֹנִי, רֹאשׁ השלושים (הַשָּׁלִישִׁים)--הוּא-עוֹרֵר
אֶת-חֲנִיתוֹ עַל-שְׁלֹשׁ-מֵאוֹת חָלָל, בְּפַעַם אֶחָת.
Whether you go with the kere הַשָּׁלִישִׁים or you go with the ketiv השלושים Jashobeam is clearly not head of any three. He is either head of the "officers" or the "thirty" but not of "three". And the Septuagint agrees with this. The parallel verse in Samuel which reads ראש השלישי doesn't pose a problem at all, since according to the Masoretic text this should not be read as "head of three" but רֹ֣אשׁ הַשָּֽׁלִשִׁ֗י which is an archaic term for "head of officers" as well. (see @ba post for more on this). So the texts in Chronicles and Samuel both point to "head of officers" as the original title of Jashobeam. Even the ESV who has "head of three" in v. 11 notes that it is not being loyal to the Hebrew text, only that the text in Samuel indicates that "head of three" is the correct title, but as we saw this is simply not the case if we go with the Masoretic version (which they simply disregard). Likewise the NLT notes that "three" comes up in some Greek manuscripts, and that Samuel likewise suggests "three". But as I said, in the Hebrew text of Chronicles there is no number three (in any of the versions), and Jashobeam clearly does not feature as their commander. Since the MT and the Septuagint both seem to agree that the text does not have a "three" then I think it would be logical to reject the ESV and the NLT's translation.
Abisahi
Moving on to v. 20 the Hebrew reads:
וְאַבְשַׁי אֲחִי-יוֹאָב, הוּא הָיָה רֹאשׁ הַשְּׁלוֹשָׁה, וְהוּא עוֹרֵר
אֶת-חֲנִיתוֹ, עַל-שְׁלֹשׁ מֵאוֹת חָלָל; ולא- (וְלוֹ-) שֵׁם,
בַּשְּׁלוֹשָׁה.
In the MT Abishai is clearly identified as "head of the three", and the Septuagint agrees with this reading. The NASB which has "head of thirty" in my opinion unnecessarily complicates matters. The problem is that in the subsequent verse Abishai is clearly described as "head of the three", so according to the NASB this would make Abishai both head of three and thirty! Furthermore, the text changes drastically from thirty to three:
As for Abshai the brother of Joab, he was chief of the thirty, and he
swung his spear against three hundred and killed them; and he had a
name as well as the thirty. 21 Of the three in the second rank he was
the most honored and became their commander; however, he did not
attain to the first three.
See how awkward the two verses become according to the NASB. But according to the majority of traditions the text flows smoothly as Abishai in v. 20 and 21 is consistently described as being the head of three.
Syriac text
I should note that the NASB's choice of "thirty" is influenced by the Syriac text. The Syriac text, according to @ba's research, indeed gets out of this conundrum by substituting "thirty" for "three" in v. 21 as well. While this ensures coherence, it differs vastly from the text of the MT and LXX which have "three" consistently throughout v. 21. The Syriac differs from the MT and LXX in other aspects as well. For example, the word בַשְּׁנַ֙יִם֙ which is present in the MT and LXX is missing from the Syriac. Similarly the end of v. 21 in the Syriac differs completely from our known text (according to @ba's unsophisticated translation it reads: and he warred like thirty), which, in my opinion, casts serious doubt on the reliability of the Syriac's text here. Indeed the NASB, itself being aware of this discord, deftly reverts back to the MT's text in v. 21 thus creating the incoherence between the two verses. All I'm saying is that the text as we know it supports Abishai as being the head of three.
So from my research I conclude that Jashobeam is most likely the head of thirty, while Abishai is most likley the head of the three mighty warriors of David.
It is mind boggling how Jashobeam is described by most bible scholars as "head of three" with little to no evidence to back up their claim.
It should also be noted that the only person clearly identified in the bible as one of the three warriors is Eleazar the son of Dodo (v. 12). The other two are never clearly mentioned by name, and though bible scholars try to identify them they are nothing more than speculations.
