The Great Armament saw a period of intensive ship-building in Númenor, and we know that Alcarondas set out with the ships of that Armament, so it is strongly implied that it was built at this time. It's origins are not given explicitly, however, so we cannot conclusively rule out the possibility that Ar-Pharazôn's ship had existed before this period.

The closest we come to a translation of the name Alcarondas, is in The Silmarillion, where the ship is named as 'Alcarondas, castle of the Sea' (Akallabêth). This does not appear to be a literal translation of the name; there is no obvious Elvish element for 'sea' anywhere in the name, but alcar means 'glory', so a more literal translation seems to be something like 'castle of glory' or 'glorious castle'.