Just as the appearance change is included in the Race Change, I believe it would make sense to also include the name change in it as well..
My reasoning is simple: if you are changing your race and if you are anything like me and have named your character with names that fit its race then you will likely also going to need a name change as well unless you are cool with having a Redguard with a Khajiit name, an Orc with an Imperial name and so on..
This would all cost $45-$50.. and that's a bit crazy..