I feel like this addition is necessary after the release of Solo: A Star Wars Story.
It is established that Han knows some Shyriiwook, and he actually speaks some while Han and Chewie are in the cage together. Later, we have Han asking Chewie his name.
HAN: So what's your name, anyway?
CHEWIE: [Wookiee growling]
HAN: Chewbacca? (CHUCKLES) All right, well, you're gonna need a nickname, 'cause I ain't saying that every time.
Read more: https://www.springfieldspringfield.co.uk/movie_script.php?movie=solo-a-star-wars-story
This is actually quite indicative, since Chewbacca is a proper noun, they've clearly never met before, and Chewbacca is not previously known to Han.
So this demonstrates that however it is that the Basic transliteration (probably better say transphonetization) works, there is some sort of mapping between the original Shyriiwook phonology and Basic phonology. I.e. One can hear a word in the original Shyriiwook and do a standard mapping into this alternate pronunciation for the rest of the Galaxy to employ.
So, that's how it is that his name is Chewbacca.