Yes, my DD10 had a huge stable of imaginary cats between the ages of 3 and 5. I wrote down all their names at one point, but there were three who were with us the most. We had to watch out not to step on them, open doors for them, etc. At the time, they sometimes got annoying, but I now look back on the phase fondly. She gave her animals the craziest names, too--my favorite was Golden Retreefrog (like golden retriever--it was a golden tree frog).