Understanding that not everyone has been in the military, I'll offer the following:
1. The M113 series has never, ever, been referred to as a "Gavin" either officially OR un-officially.
2. In my career, I heard them referred to as M113s, '113s, "tracks", "PCs", or "ACAVs" (Vietnam usage). No manual or document I ever saw used the name "Gavin".
3. The name "Gavin" appears to have been invented by an internet personality who pushes it on others while driving a personal agenda. I consider this an insult to Gen. James M. Gavin, who was a great airborne leader.
It is common for people to get confused by the name, and to assume it is real/true. It's not their fault, and we can only hope to educate.
It's also a shame that this "name" still pops up now and then. I thought it had been laid to rest also.