I wonder if basa is an adaptation of the Japanese word (basa) used to describe a swish or pfft sound of something striking but making a soft noise. I forget which of us it is that is more familiar with Japanese, (is it Branson?), maybe he can corroborate.
No idea about a Japanese connection. We'll need a history check on the origin. Garland's web pages notes:
"Six face types are available: rawhide, copper, urethane, nylon, Gar-Dur plastic and BASA. The BASA hammer has been the leading refractory hammer for decades. Used for installation and demolition of coke ovens, blast furnaces, and other applications where refractory brick (firebrick) is being installed or removed."
"BASA brand trademark GT&C Inc" is found on their specs for a hammer using BASA faces, as opposed to copper, rawhide, nylon, etc.
So BASA is the name of a material, one which is chiefly designed for refractory work -- building industrial fire boxes.
Refractory building requires that there are no voids in the mortar between the fire bricks. "All joints must be completely filled over the entire surface with joint material." And, "Rubber and plastic hammers of different sizes [are used to] align the laid bricks and to close the vertical and bed joints. The bricks will not be damaged even when hit hard if working properly with these hammers."
I'd guess that they developed BASA early on as a material, and that gave the hammer its name, since BASA is only one of the materials used for the faces, and that the other materials were added later.