Trying to be a bit more objective in the approach to the debate, you actually need to look at the etymology of the word. The first real use of the word dates back to Roman times and the word Nigrum or Niger which means black or dark. As many western languages are based upon Latin then it doesn’t seem surprising that the word is prevalent in English, Spanish/Portuguese (negro), French (nègre), Dutch (neger) or Italian (nero). There are also various forms in the English language - namely niger, nigger, neger and negar.
Well before the Slave Trade and the racism that ensued from the period, the word was used in various texts from the 1500s. The earliest known published use of the term dates from 1574, in a work alluding to "the Nigers of Aethiop, bearing witnes”.
The use of the word ‘nigger’ as derogatory term developed later In the late 18th Century alongside the established use that had been ongoing for literally millennia before that (that being in reference to a dark or black colour). It was used to put down people with African origin, mostly in the Americas, and that is where the offensive use remained for many years. It probably reached it’s pinnacle of awareness in the racial context in the 1950s and 1960s with the work to end segregation in the USA.
So, it really comes down to intent. If Gibson named his dog ‘nigger’ as he saw it as a way to put down people with black skin, then that would indeed be a racist intent. However, if he named his dog ‘nigger’ due to the Latin derivation and the fact the word, at that point, had not become such a word of abhorrence amongst many today, then that is a different matter. As others have said, we cannot erase history, and we shouldn’t - if amongst Gibson’s memoirs we find that the naming of his dog was with racist intent then of course it should be called out and the name removed. If not, the dog’s name should remain and people should be educated that there are 2 contexts to the word ‘nigger’ - one which dates back thousands of years to the Latin language and the other, which is with derogative intent, should never be used.