I am in the middle of writing my rough drafts for the Common App essay; I decided to answer prompt #1. I am writing about a disorder that I have, and how my condition has impacted my future goals and plans. Throughout my childhood (and even now) I go to a children’s hospital for my appointments. The children’s hospital and my condition have affected my life in a big way. Is it okay to mention the hospital by name in my essay? Can I talk about how going to this hospital for my condition has inspired me to work at this children’s hospital when I grow up? I’m planning on talking more about the positive effects the condition has had on me, not solely about the actual condition itself. Thanks for all the help! 
Sure. You can use names (though people usually use first names only), dates, places, products, etc., since it’s a story about your actual life and you aren’t disclosing anything private / personal.
I don’t see how writing about a specific place would be a bad idea. If including it will help you tell more about yourself, then go for it.
If you say “St. Judes” or “Betty Ford” or “Mayo Clinic”, I have an immediate idea of what you’re talking about. It saves you a lot of words of explanation, words that you can use to showcase what the essay should be about: you.