"beech," "beech tree"
14th cent. From Latin fagea "beech wood," an adjective from fagus "beech tree." Why the word in Spanish was drawn from the adjective fagea and not the noun fagus is rooted in the gender system of the language. Latin boasted a complex gender system where words ending in suffixes like -us could be masculine or feminine, but there was a strong tendency across Vulgar Latin speakers to simplify things by interpreting -us as universally masculine and -a as universally feminine. The names for trees in Latin, which were mostly feminine -us nouns, were reshaped to be "grammatical" in Vulgar Latin by changing the ending to -a. However, when there was a need to distinguish the tree from its fruit, Vulgar Latin speakers minted their word by drawing from the feminine adjective instead. See also Penny (2002).
From Proto-Italic *fāgo- 'id.' From Proto-Indo-European *bheh2g-o- 'id.'
Also the origin of the surnames de la Haya, Hay, Hayas, Faya, and Fayos.
Asturian faya, Portuguese faia
Gaulish *bāgos "beech"
Old Norse bók "beech," Old High German buohha 'id.,' Old Saxon bōka 'id.,' Old English bōc 'id.' (English beech)
Ancient Greek φηγός (phegós) "oak," "acorn"