A word appearing as G. {nort >>} nost in the Gnomish Lexicon of the 1910s with three distinct meanings: “birth”, “blood = high birth” and “birthday”, though the last sense also applied to the word G. {noss >>} nôs (GL/61). It is clearly based on the early root ᴱ√NŌ “become, be born” (QL/66). G. nosteg seems to be an adjectival variant in the phrase dana nosteg “birthday = ✱day of birth” (GL/61)
Neo-Sindarin: The usual Neo-Sindarin word for “birth” is ᴺS. onnad, gerund of the verb onna- “✱to give birth”; I’m not sure who coined this neologism, but it has been in use for some time.
A noun in the Gnomish Lexicon of the 1910s glossed “kinsman”, a combination of G. nôs “birthday” and G. ged “†kinsman” (GL/61), hence probably “kinsman by birth”. In one place it appeared in the form nosged, but this was deleted and replaced by nosied (GL/38).