Eldamar: The root
In section VI, Dwellings in Middle Earth, in The Nature of Middle Earth, the principal forms were mbār(a), (uninflected or inflected), and the derivative form, mbardā.
Formerly, it was used in Quenya with the archaic form, már, as a defining genitive (possessive) or genitival compound.
When it’s added to a personal name, or a family residence, it also includes the adjacent lands such as the main settlements of the lands, in this case.
When this is applied to houses, eldamar then becomes elvenhome, as they were at home and remained united as Elves.