Definitely go with the English names where applicable. The fact that the Rōmaji Name is mentioned in the profile is enough.
Desutegoro is his actual name, because in the official japanese character page of my hero every hero has their japanese and english names, and deatharms has "Desutegoro" written as his english name.
If that's his actual name, then that's fine.
EDIT: Though his profile should probably mention in the introduction or infobox what his hero name is.
Personally I like using "My Hero Academia" because its the official english translation and "Boku no Hero Academia" is not translated correctly to english. Its the same reason Viz, Crunchyroll and Funimation do not use "Boku no Hero Academia".
I dont think it would matter that much since both http://bokunoheroacademia.wikia.com and http://myheroacademia.wikia.com lead to this wiki.