However giving it the name 'Hibernia' would imply some ancient roman given legitimacy to the people of Ireland and probably wouldn't be preferred by a more anglicized Ireland with a Cromwell's England.
Using Ireland seems to me most likely, that or simply not using the name Ireland at all but rather splitting it into 4 republican territories/departments/provinces/areas, and using the names of the Cuige themselves, perhaps more anglicized.
But honestly, a lot lot lot lot lot of Irish words, Irish placenames, and Irish people names are already anglicized, even if your Cromwell's England preferred to emphasize the anglo-saxon in anglicized, and tried to make the hiberno-norman namings of places disappear.