First of all, I doubt Amaterasu sounds good. This happens mainly because of the noticeable difference between that name and the others.
Also, naming an extremely important ship "Amaterasu" is basically carrying on with the Icanus' main issue - the name. Why would be the symbol of Terran pride and hope have a totally unknown name everyone would ":wtf" at? It's much smarter to use names of prominent importance.
Maybe there are some japanese people still alive? Maybe some of them pushed that name through? Doesn't matter much, though. I like the name, you don't. Let's leave it at that.
You'd have to partially exclude Boadicea and Iceni from the list, because those two names are connected to Latin and Roman culture.

From wikipedia: The Iceni or Eceni were a Brythonic tribe who inhabited an area of Britain corresponding roughly to the modern-day county of Norfolk between the 1st century BC and 1st century AD.
Boudica (also spelled Boudicca), formerly known as Boadicea and known in Welsh as "Buddug") (d. AD 60 or 61) was a queen of the Iceni tribe of what is now known as East Anglia in England, who led an uprising of the tribes against the occupying forces of the Roman Empire.
More connected to celtic culture, IMHO.
As for Leviathan:
Leviathan, is a Biblical sea creature referred to in the Old Testament (Psalm 74:13-14; Psalm 104:26; Job 41; Isaiah 27:1). The word leviathan has become synonymous with any large sea monster or creature. In the novel Moby-Dick it refers to great whales, and in Modern Hebrew, it means simply "whale".