In your pics there are two different seat backs... Is the bottom one the high-back style with the support "staves?"
Is it still available?
I understand Hobie no longer has these available, but you may find one on ebay or through a dealer who has old inventory. Fortunately I bought some a few years ago to use on all my boats.
Note, there were a few that had aluminum staves rather than fiberglass. These were recalled -- are easy to recognize by bending the seatback over your knee -- they stay bent and are no good.
what is the proper designation for it?
They are the only seat with fiberglass staves, no lumbar support, built through 2006. They usually came with a large removable accessory packs with bottles clipped to the seat back as shown here (top):
Hobie also made a similar but differently shaped seat for their non-Mirage paddling boats. These are not interchangeable the Mirage boats. Good luck finding one!