In the beginning, way back in the far-flung times of Proto-Indo-European, the word for "it is" was something like *h₁ésti, and it had a fairly regular present participle, *h₁sónts. In Latin, these forms evolved into est and sōns, respectively (vowels get lengthened before -ns). The latter is where we get forms like absēns > "absent" and ...
In the oldest stratum of loan words Semitic t and k are generally represented by τ and κ, while the emphatic stops ṭ and q are represented by θ and χ. Witness the names of the letters tau and theta. In later loan words Semitic t and k are generally represented by aspirated θ and χ, while ṭ and q are represented by unaspirated τ and κ. This probably has to do ...
There are quite a few, actually. Just to add some more examples:
πράττω "do" (impv. πρᾶττε shows the length)
ἤλλαγμαι, pf. m./p. of ἀλλάττω "exchange"
ἡλλόμην, impf. of ἅλλομαι "jump"
Note: this answer is pure speculation (or original research, if you're feeling generous), not backed up by any scholarly references.
Neither Varro nor I marked vowel length in our Hebrew and Aramaic transcriptions. But what if we go back and add that?
מְשִׁיחַ məšīaħ → messias
יֵשׁוּעַ jēšūaʕ → iēsūs
אַבְשָׁלוֹם 'abəšālōm → abessalōm
הוֹשֵׁעַ hōšēaʕ → ...
The Greek ἀήρ seems to have entered (post-Biblical) Hebrew via Aramaic ʼwwyr. Syriac Aramaic also has the more Greek-looking form ʼʼr. The replacement of an intervocalic glottal stop by a semi-vowel (here: ʼāʼer > ʼāwer) is typical of Aramaic, and other Semitic languages.
The Italian Wikipedia page on Roman onomastics states, without references though,
Former auxiliary soldiers and other categories of people that earned the Roman citizenship, could and often would keep at least a part of their original name. A good many names (cognomina when assuming the tria nomina, but old personal slave names) were of Greek origins, ...
I think you answered this question yourself with the humble word "also" in the second sentence. "Nomen" has two meanings in Latin, "name" and a particular part of a Roman tripartite name. Even barbarians have names and there is no other word for this than "nomen".
The vast majority of Semitic words transcribed in Latin come directly from Punic; Krahmalkov provides a summary of the conventions in his Phoenician-Punic Grammar.
g, d, l, m, n, r were transcribed as g, d, l, m, n, r
'Aleph and `ayin were completely ignored in transcription, and went silent at some point in Punic history
b was transcribed as b; later, as f ...
I think that TKR's remark on the occasional spellings with υ may also be relevant to the matter. Note that in Ἰησοῦς with the single σ, the the ש is in the vicinity of a rounded vowel.
Also interesting is that while שְלֹמֹה (Shelomo/Solomon) is Σαλωμῶν (or a variant), אַבְשָׁלוֹם (Abshalom/Absalom) is Αβεσσαλωμ, with medial σσ. Also note אֲבִשַׁי (Abishai)...
I take it you're not interested in later words like sultanus, algebra, alcohol or nadir. Then I hope that this article from 1892 isn't too outdated: 'On Semitic Words in Greek and Latin' by W. Muss-Arnolt (https://www.jstor.org/stable/2935792?seq=1#metadata_info_tab_contents). If you search for "lat." within the pdf, or look in the index at the end, you'll ...
I just recently stumbled across two examples in Lewis and Short of semitic words, for which L&S cites no Greek intermediary. Of course, the lack of citation itself is not exactly proof that Greek intermediaries do not exist.
The two words are manzer from the Hebrew, and mapālia from the Punic, conveniently located adjacent to each other on the page.