Yes, I have several fish I know I have caught multiple times in my life, and know some fish that not only did I catch, but others did as well. The biggest fish I caught at the Idaho fish-in this past season came to hand twice, from the same spot, on the same fly, a couple days apart. One big brown in Montana I caught four times in one season, and I have pics of at least two of those days. I have caught steelhead twice in the same day, and once on the San Juan in NM, my ex, my brother in law, and I caught one trout four times in a single day.
Photos really help with this, as fish like browns have unique spot patterns that can be used to identify them. Scars and such (like the bow on the Juan) assist as well.