VW had a hard time asserting itself in the US market at the beginning; VW Bulli and Beetle were bestsellers, but the Karmann Ghia etc. were not intended for the US market.
There are and have been so many beautiful cars - you can't know them all.

Karmann was an automobile and body construction company based in Osnabrück. Karmann manufactured complete vehicles, especially convertibles for VW and other - for example Rabbit Cabrio.

I found this car on a website, and possibly a nose-on pic. It is a 1965 Karmann Ghia Type 34. Not offered for sale in US.

Just found this on internet, it was derived from type 34: prototype VW Karmann Ghia 1600 TL (1965)

I've never seen a fastback version like this.