§ Rhimbron (TI:227) >> Rhomrin, Romrin (TI:236)
§ Rhimlath >> Rhimdir (TI:240)
These are the names of Haldir’s brothers, the first one later becoming Rúmil and the second one Orfin, Orofin and eventually Orophin.
Rhimbron may contain the initial element #rhim- from the stem RIM- with N. rhemb, rhem ’frequent, numerous’, rhimb, rhim ’crowd, host’ and #-bron from BOR- BORÓN- with ON. boron ’steadfast, trusty man, faithful vassal’ (> N. bór), brono- ’last, survive’ and so on. Hence the name might be interpreted as *’he who endures a lot’, perhaps in analogy to Rimbedir above (1.3). Remarkable is the appearance of the element her ’host, army’ in Germanic names as Hermann, Walther; and rhim(b) ’crowd, host’ might play a similar role here. Alternatively we should, as in the case of Rimbedir, consider RIP- ’rush, fly, flying’, N. rhimp, thus *’rush-endure’. Many Germanic (and also Elvish) names are in fact put together similarly, out of two elements with or without an apparent connection to each other. But possibly -b- still belongs to the first element, while -ron is a name suffix; compare N. callon < kalrondō ’hero’ (KAL-).
R(h)omrin looks like an adjective from N. rhom ’horn, trumpet’, but -rin may also be a name-formative suffix.
For Rhimlath the best word in sight is N. lhath ’thong of [?leather]’ (LATH-), perhaps in the sense of ’bow-string’, thus *’rushing/fast bow-string’?
Finally, Rhimdir contains suffixed N. †dîr ’male, man (elf, mortal, or of other speaking race)’ surviving chiefly in proper names (DER-), so it might be *’the rushing one’.
However, these are just speculative suggestions. It is very well possible that these names do not bear a significant meaning at all, or at least not all of them.