I think there's a case to be made for both, she used K-den-live because almost every KDE based program is called kSomething like it's the 90s, but if it starts with KDE then its referring to the KDE suite "brand" so it could be KDE-N-Live as well.
Every fucking time I see it I think of it as K-Eden-Life or K-Eden-Lite which is incorrect for several reasons