"Well, if we remember what each of the fish look like, we can describe them to the merfolk. And if they don't have any idea what we're talking about, then obviously it's undiscovered and we can name it whatever we want!"

This isn't a very good idea. However, it's the best idea that Strange has. He doesn't have any sort of other way to mark what fish they've seen on him right now (the notebook and pens he owns are back in his trailer) and he's got no idea if any sort of magic could serve their purpose. So, memory it was.