Our name Halcydon is a variant of a halcyon, a kingfisher. This bird has very special meaning to us; while were discussing whether or not to add this domain to our portfolio, and belted kingfisher flew into our window!
Here is some more information about Halcydon as recorded by the Oxford English Dictionary (O.E.D.):
In classical mythology: a bird, usually identified as a kingfisher, which brooded around the time of the winter solstice in a nest floating on the sea, charming the wind and waves into calm. In later use also (chiefly poetic): a kingfisher, esp. the common kingfisher. The alteration of Hellenistic Greek ἀλκυών to ἀλκυδών may also have been influenced by a folk-etymological association with ancient Greek ἀλγηδών pain, grief: in classical mythology Alcyone (Greek Ἀλκυόνη), the daughter of Aeolus, was overcome with grief at the shipwreck of her husband Ceyx, and transformed by the gods into a kingfisher (Greek ἀλκυών) (Hyginus Fabulae 65).
Aside from the mythological bird, halcyon has also become popular for the following definition, also from the O.E.D. :
A period of calm, happiness, or prosperity; (as a mass noun) calm, tranquillity. Also: a period of calm or pleasant weather
Here is a reference to Halcydon in an older text: 1648 A. Ross Mystagogvs Poeticvs (ed. 2) viii. 143
The Halcyons or Halcydons were said, I think, to be begot of Lucifer, because these birds begin to chirp or sing about break of day, at the rising of Lucifer, or the morning starre.
For great article on the symbology of the kingfisher, read Take on Nature: Why the kingfisher is known as ‘the halcyon bird’.