"Grug" in this context basically just means a kind of simplistic caveperson-like mindset.

For whatever reason, the sound "Grug" is associated with cavepeople in English.

Grug was a caveman character in a movie, I figured that's where the name came from.

Seems to be a reference to "The Croods" [1], a 2013 animated movie in which Nicholas Cage (!) voices the caveman Grug.

[1]: https://en.wikipedia.org/wiki/The_Croods

Grug is simply the narrator's name. He's speaking in the third person.

Meant to be some generic "caveman" name/character.

Whenever I run into such a problem I use google (or the web search of your choice). You may not have expected it (and you won't always be this fortunate), but this immediately makes the identity, nature, and meaning of grug evident.

This is one instance where an AI might shine. Ask it to summarise the article in the style of an articulate intelligent person.

grug is grug name

grug neighbours ugg, oog, thog, thag, tragg, yog, grr, argh not use computer

https://tvtropes.org/pmwiki/pmwiki.php/Main/HulkSpeak

search for a plain english translation, it's out there