I'm aware that Beagle borrowed the name from a Greek goddess by the same name, but I cannot determine a connection outside of that (Wikipedia's entry is also rather short, and I can't seem to find anything better on my own). I get the feeling the name is supposed to evoke a motherly feel for the character, but I'm curious about what other significance this name has for the character.
This was directly addressed by the author in an afternote in the new Deluxe ebook edition of The Last Unicorn.
Connor: Let’s talk about character names, then. Your readers have been speculating about them for decades. When the unicorn becomes human, and Schmendrick calls her the Lady Amalthea—where did that come from?
Peter: It’s funny about the names, because at the time they just came to me, and mostly I didn’t realize why they were appropriate until later. Amalthea sounded good, and I had some vague recollection that it came from Greek mythology—it’s the name of the goat who nursed the infant god Zeus when he was being hidden from his father, who wanted to eat him. This wise goat fed the baby, sheltered him, and played with him. But at the time I decided to use the name, I’d forgotten the rest of the story—that when Zeus got older and was acquiring his full godly strength he became too much for the goat to romp and wrestle with, and at some point he accidentally broke off one of her horns. He was immediately apologetic, of course, and turned the broken-off horn into the cornucopia—the Horn of Plenty. But Amalthea only had one horn from then on, so in a real sense she was the first unicorn.
According to Britannica, Amalthea is sometimes represented as a goat (or possibly a nymph goatherd) who raised the young Zeus, and tore a horn off of her own head (or one of her goat's heads) to make a cornucopia.
For someone versed in the classics, this would be a most appropriate name for someone that you wished to associate with both high levels of femininity and, critically, the possession of one horn.
Amalthaea, in Greek (originally Cretan) mythology, the foster mother of Zeus, king of the gods. She is sometimes represented as the goat that suckled the infant god in a cave in Crete, sometimes as a nymph who fed him the milk of a goat. This goat having broken off one of its horns, Amalthaea filled the horn with flowers and fruits and presented it to Zeus, who, according to one version, placed it, together with the goat, among the stars. In general, the horn was regarded as the symbol of inexhaustible riches and plenty and became the attribute of various divinities and of rivers as fertilizers of the land.