Can I (should I) change the name of this distribution?

Actually changing the name because someone might be offended by a sound that comes from a completely different domain and is completely separate from the history of racism would be condescending, in my view.

And, as you say, the term is in common use. Changing it would also confuse some people.

Leave it be.

There was no intention to do harm and the acronym is natural. The language police are unlikely to chase you down. It would be different of course if the acronym were chosen for racist purpose, but that is clearly not the case here.

If you are at all unsure about causing offense, you could always use the full name in your paper "Normal-Inverse-Gaussian distribution". It won't be any less readable for that.

In your code pick a different prefix that still clearly identifies the distribution, e.g. ninvg_foo().

Change the name if you like. Point it out prominently in your paper and code, possibly more than once (e.g. first mention in the main text and in the methods / supplement, of course also in the function documentation, etc.). The names of even common objects are changed for a variety of reasons. It happens, and people should be aware that names are usually pretty arbitrary.

Example: I once read a book where the discrete-time Fourier transform (DTFT) (by all means the standard name) was called DSFT (Fourier transform in discrete spaces), because, technically, it can be computed over other domains than time. It was weird for a moment, and then I got used to it, and know I'm kind of glad that the authors stressed this point because it made me think about something important.

Conventions exist until someone begins to challenge them. I'm scared of the language police (see another answer here) doesn't even need to be part of the justification. It can just be that another name sounds better to you. Of course, standard names shouldn't be changed on a whim, but they can be (and are).