"a hill of moderate elevation and more or less rounded outline," Old English dun "height, hill, moor," from Proto-Germanic *dunaz- (source also of Middle Dutch dunen "sandy hill," Dutch duin), "probably a pre-insular loan-word from Celtic" [Cambridge Dictionary of English Place-Names], in other words, borrowed at a very early period, before the Anglo-Saxon migration, perhaps from PIE root *dheue- "to close, finish, come full circle."
The more general meaning "elevated rolling grassland; high, rolling region not covered by forest" is from c. 1400. Specifically of certain natural pastureland districts of south and southeast England (the Downs) by mid-15c.
The non-English Germanic words tend to mean "dune, sand bank" (see dune), while the Celtic cognates tend to mean "hill, citadel" (compare Old Irish dun "hill, hill fort;" Welsh din "fortress, hill fort;" and second element in place names London, Verdun, etc.). German Düne, French dune, Italian, Spanish duna are said to be loan-words from Dutch.