Ther are not *sedenions* because sedenions are not associative: https://en.wikipedia.org/wiki/Sedenion

I doubt they have a name but this algebra is well understood. The hyperbolic quaternions is just $M_2({\mathbb R}$. You take a tensor product of them with usual quaternions ${\mathbb H}$. As a result you get $M_2({\mathbb H})$ that deserves no special name.