If I'm understanding this correctly, you could easily just put the logos on different layers and hide the ones you don't want. Use folders to get it tidy. Not a drop down menu, but I'm not aware of photoshop having that kind of capability.
This is off topic, but I was unaware of black squirrels association with Kent State and went down a rabbit hole on them. My lifelong best friend was named after a family friend of his dad's who allegedly was responsible for introducing black squirrels to Iowa. It was always a quirky story that he told a lot and he just found his namesake funny. Turns out, not true at all and not really a unique story either. I probably should keep it to myself and let him keep the story lol