ENT stands for Ear, Nose, and Throat, referring to the medical speciality of otorhinolaryngology; also referred to just as orolaryngology, probably because if you're treating the ears and the throat (larynx) you're bound to make some sort of passing inspection of the nose as well.
In cryptic crosswords, the words 'hospital department' invariably code for the letters ENT.
Tolkien's name 'ent' is an Old English word for some kind of ancient giant. An expression like enta geweorc 'work of giants' occurs in several places: in Beowulf, the ancient sword Beowulf uses to kill Grendel is called enta ær-geweorc 'ancient-work of giants' (and wundor-smiða geweorc 'work of wonder-smiths: no clumsy dumb giants these). In The Ruin it's used of the Roman ruins at Bath. In The Wanderer it says eald enta geweorc idlu stodon 'old work of giants stood empty'. The word entisc 'giantish' also occurred.
The most striking Tolkien reference to ents in Old English is the line in The Cotton Gnome (don't get excited, Cotton was a collector and a gnome is an aphorism), orþanc enta geweorc 'cunning work of giants', which gave Tolkien the name Orthanc, Saruman's tower.
But Tolkien made his word appear to be related to the Elvish: the Sindarin is onod, plural enyd, collective plural onodrim. (Tolkien in his letters remarks that the plural ened, though less accurate, could also have been used in Gondor.)