There is an Old English name Hæleþ meaning 'warrior' or 'hero' (or simply 'man') that Tolkien modernises as 'Haleth' for the name of one of Helm Hammerhand's sons. That origin is appropriate in that context, but the same etymology is much more difficult to assign to Haleth of Brethil. It may be that Tolkien was inspired by this Old English term (in the first tellings of the story, the character of Haleth was indeed a heroic Man). Internally within the story this cannot be the name's origin, however, and so all we can realistically say is that the meaning of the name is unknown.
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