For a second I went "Seungkyun??" But you mean the boat i am guessing.
In all honesty I have thought about it once but never settled on anything. But now i have :]
Yuto didn't changed the name when inheriting it, he didn't care that much, and one doesn't just /change a name of a ship on a whim/ it brings bad luck, so it's a name his parents gave to it. But doing some digging, the name: Nehalennia, seems nice to me.
Its a sea goddess with little known about them but their place of worship was found in my country and more things are based on mine and surrounding countries so it would be fitting. In theme but a little mysterious? Sounds right.

(Jaeyoung's own vessel he'd name something simple but with a hint as to why he got it. So i think he'd name it Dawn's Hope)