http://www.uesp.net/wiki/Tamriel:Eraintine#Eraintine
The Bosmer proved to be too undisciplined and prone to desertion for furthur use. They would sometimes walk into the shade of a single tree and vanish. Their forest-coupling skills are remarkable. The title of their most famous poem, the 'Meh Ayleidion', means, 'The One Thousand Benefits of Hiding'.
That makes it pretty clear that "Ayleid" means something like "Hidden", making a latter-era Wild Elf name for themselves. What might the Ayleid have originally called themselves? Something-mer no doubt. They had a high opinion of themselves, so maybe something like Malamer (high elf in Ayleidoon), Adomer (lordly elf), or Arpemer (noble elf.) On the other hand one of the text fragments from the mage's guild quest references "our exiled elven ancestors" so they might have a name related to exile: Meldimer (driven elves), Abamer (forbidden elves). Sun, sky, and stars were important in their culture, so maybe something like Varlamer or Kynmer.