Gunnarr comes from Old Norse. "Gunnr", which means fight/combat in Old Norse, and "arr", which relates to warrior in Proto-Germanic.

Áskunnr Gunnarskólinn has three elements: The obvious Áskunnr but also "Gunnr" and "Skólinn". The genitive of "gunnr" is "gunnar", hence the composed word "gunnarskólinn" which translates to the The School of Combat.

Two notes: It is not school of Gunnar (the male name), which would have been "gunnarsskólinn". Also, it is specifically "The School of Combat", not "school of combat", which would have been written as "gunnarskóli".