What is a flan pan called?

I love making (Filipino) leche flan for my wife and I. However, I use a 9" round cake pan that I wedge into a 9"x13" cake pan, which I fill with water until it just touches the bottom of the cake pan. I then sprinkle a bit of cinnamon into the water, pour my flan mix (10 egg yolks, 1 can condensed milk, 1 can evaporated milk, dash of vanilla) into the round cake pan, and cover with aluminum foil to create a sort of rudimentary bain marie. I then pop this into the oven for 30 to 40 minutes.

My question though is: is there a pan specifically for making flan? If so, what is it called? My way creates a very top heavy and unstable (water sloshing) platform - and I'm afraid I might one day spill hot water on myself - not to mention that getting the round cake pan out of the rectangular cake pan is a pain.