To add, the following is from Hammond And Scull's
The Lord of the Rings, A Reader's Companion...
'In Appendix F Boromir is said to be a mixed form (...), that is, containing both Quenya and Sindarin elements (Sindarin boro(n) 'steadfast' + Quenya míre 'jewel').' H&S (partial quote)
And later (they don't even try to explain the first element in
Faramir).
'The second element of Faramir is probably the same as that in Boromir, Quenya míre 'jewel'. H&S
This interpretation of Boromir is based on the name as it was interpreted back in Etymologies (part of the Etymologies entry also appears in the H&S entry) under the base BOR- 'endure' (and BORÓN-) where Tolkien refers to the ON word
boron (pl. boroni) 'steadfast, trusty man, faithful vassal' and refers to the N. names given to the 'Faithful Men'
Bór, Borthandos, Borlas, Boromir. And JRRT adds that the name
'Boromir is an old N. name of ancient origin also borne by Gnomes: ON Boronmíro, Boromíro: see MIR' (and under MIR the name
Borommíro is scribbled in).
Though this is earlier stuff it appears that the word
boron 'survived', noting that in
Cirion And Eorl we find a character named
Borondir for example (*boron + ndir). In any case, in the old idea a word for 'hand' was not involved, and as I say, I doubt it was later by the time
The Lord of the Rings was published.
H&S note that Arden Smith (generally) advised them on linguistic matters for their Reader's Companion; and were also indebted to Carl Hostetter, especially for his editorial work on Tolkien's essay
The Rivers and Beacon-hills of Gondor in
Vinyar Tengwar. And although that doesn't mean Mr. Smith or Mr. Hostetter wrote these particular entries, I would say both entries represent just about the best we can do to date, without going too far down the path of speculation anyway, given the information currently available with respect to these somewhat difficult names.