The elements of Cirion's name are not difficult to parse, but their combined meaning is difficult to interpret. Cir- literally means 'cut, cleave', but was often used figuratively to mean 'ship', while -ion usually means 'son'. Given that his father Boromir died early due to a Morgul-wound, the name Cirion may imply something like 'wound-son' (that is, 'the son of Boromir who inherited due to his father's wound').
The alternative 'ship-son' is perhaps the more natural reading, but we have almost nothing in Cirion's biography to associate him with ships. The exception is a brief reference that his coasts were harried by Corsairs during his time as Steward, though this hardly seems significant enough to commemorate in the Steward's name.