I've gotten this question a couple times now so I'll lay out the reasons why "cool" is incorrect.
Let's break this down:
グッドクルカイザー guddokuru kaizaa
グッド good (guddo)
クール cool (kuuru)
Now, while クル and クール look almost the same, that elongated syllable makes all the difference. A native Japanese speaker would never use the shorter kuru instead of kuuru when trying to say "cool". It's like "mod" and "mood", in English, visually they're similar but you'd never mix them up.
The name is a pun on グッとくる (guttokuru), which is Goody's catchphrase. I've been translating it as "Good Feeling" although honestly that's a bit of a simplification solely for the subs. The dictionary definition is "to touch emotionally; to feel something; to strike home". TBH now that I'm thinking about it, I probably should have translated his catchphrase as "all of the feels!" although I dislike using modern slang that might pass out of favor in a few years. It's a very emotionally charged phrase, so while "Good Feeling" isn't the best, it uses the word "good" and it gives you a general idea of the nuance, although we've lost the pun.
tl;dr you can't read クル (kuru) as "cool" and it's a pun so "Good Cool" is a mistranslation.
