AMD named their memory fabric "infinity fabric" for marketing reasons. So when they developed their memory attached cache solution (which lives in the memory fabric, unlike a traditional cache), the obvious marketing name is "infinity cache"

The main advantage of a memory attached cache is that it's cheaper than a regular cache, and can even be put on a seperate die, allowing you to have much more of it.

AMDs previous memory fabric from the early 2000s was called "Hyper Transport", which has a confusing overlap with Intel's Hyper Threading, but I think AMD actually bet intel to the name by a few years.