This type of buffer is called "diamond buffer" but I don't where the name comes from. I have also seen the name "Jung Super Buffer" (from his article). Many IC's have this diamond buffer, LT1223, BUF634, LME49600 and many more.
This buffer can be used in a preamp as line stage without gain, as a buffer for DAC's and CD-players. You can also use it for driving headphones. The buffer is rather small and very thin so it can be placed in narrow spaces.
There are lot's of good info out there on this subject. Walter Jung has written a couple of good articles and one of them is about this particular buffer. In fact his article is THE best for a normalDIY'er.
Realizing High Performance: Buffers (Part I)
Realizing High Performance: Buffers (Part II)
The ancient LH0002 is also a simple diamond buffer. The equally ancient LH0033 consists of a JFETbuffer.
AN-47 from Linear is a big document, very well written. Look especially at page 45-47. Those pages describes a discrete diamond buffer.
AN-227 from Texas Instruments is also worth reading.
This Texas document has also a part about diamond buffers.