Are the names in this chapter some sort of puns?
Sort of, yes. There is a Japanese golfer called Ishikawa Ryo. Ishikawa is the name of a prefecture, so Kuroha named the three Ryos here after other prefectures/regions of Japan (Fukui, Toyama and Ishikawa are all prefectures in the Hokuriku region).
Ishikawa Ryo does apparently also have the nickname of “Bashful Prince,” hence Fukui being the “Prince of Golf,” while at the same time being a reference to The Prince of Tennis.
Cheetah Woods is just Tiger Woods.
I dunno about Taguchi. Or Saru. Lacking research.