As a real name, 'Yale' comes from the old Welsh word iâl, referring to fertile uplands or hill country. It's not completely clear, however, whether Tolkien meant this same derivation to hold. One problematic reference is a mention of the 'lowlands of the Yale' in The Fellowship of the Ring I 3, Three is Company, which seems to contradict a derivation from 'uplands'. What's more, Tolkien originally considered calling this region 'Northope' ('small northern valley') which again casts doubt on a connection to hill country.
Though a derivation from Welsh is unusual for a place-name within the Shire, it might conceivably hint at a connection with the Brandybuck family. Tolkien consistently translates personal names within that family using old Welsh elements, and we know that they originated in the Marish on the borders of the Yale, so perhaps this implies some kind of ancient historical association.
Alternatively, Tolkien might have had some entirely different derivation in mind, though if so he left no clues to what that derivation might be. There are few realistic candidates, but one possibility might be Old English ealh a place of shelter (though this normally referred to a building, rather than an area of land).
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