The etymology of Carn Dûm is uncertain and it could be any it could be any Elvish or Mannish language. Concerning Mannish and the real world languages, it could be Gaelic, in which it roughly translates as "mountain fortress"; although Tolkien uses Celtic elements for some translated Mannish names, this would have been the only instance where he uses Gaelic. It is unknown whether this is just coincidence or not. Dûm is a Khuzdul word meaning "halls, mansions". The name Carn Dûm therefore could be Khuzdul (suggested by its proximity to nearby Gundabad) but Tolkien used K for this language instead of C. In The Return of the Shadow, "Carndoom" appears as an early name of Dimrill Dale which, according to Tolkien, means "Red Valley". This corresponds with Sindarin carn "red" and tûm "valley". David Salo favors the Sindarin interpretation of "red valley", and provides the name as an example of the few Sindarin phrases where the adjective precedes the noun (others being Sarn Athrad and Sarn Gebir). Otherwise, neither words carn and dûm have been attested (carn could be a short form of caran possibly also seen in Carcharoth, "red maw")
Sindarin
carn dûm
place name. ?Red Valley
Chief settlement of Angmar (LotR/146). The language and meaning of this name is unclear, but it is often suggested this it is Sindarin, a combination of caran “red” and a lenited form of tum “valley” (as suggested by David Salo, GS/371). The name may be debased Elvish, like the name of its kingdom Angmar, since a noun would not ordinarily be lenited in this position. The name also resembles an early (rejected) name N. Caron-dûn or Carndoom “Red Valley” found in Lord of the Rings drafts from the 1940s, and could be a re-emergence of that name (RS/419, 433).