So they have released the 4 classes and their names. Are these names the same for all alliances? Every alliance has a dragonknight? Or is it going to be like SWTOR and they will be the same class but have a different name?

Its appears they are all the same yes. In older hands-on preview they got to play Ebonheart characters and called the classes by what we know them now. This most recent round of hands-on the reviews played Daggerfall Covenant characters and again the same class names were used.

Would have preferred each faction to have its own class names, same classes and mechanics just different names. However if the class system truly is as open as its being described what the base class is called is of little consequence as we will be making classes that vary widely and I'm sure we'll come up with our own names for our class builds and such.

For example I want to play an Archer type, so I'll probably pick Nightblade and develop my Bow skills from there and will call the build Night Archer or some such. After I get to build it the way i want what the original class name is won't have much meaning.

Before people ring in with their thoughts of different class names per alliance, I don't think having the same class name is a problem. All of the races share a lot of similarities including (but not limited to) the gods they worship, the language they choose to speak, lands they originate from, etc. Not to mention that they've all been interacting with each other for a few thousand years. It's not really a stretch of the imagination to believe they would have the same names for much of their professions.