Thing is, Teddy is so wrapped into the term Teddy Bear now that you might be able to get away with it with many different names. Like my son, he looks like Winnie the Pooh. Could I call him Teddy because of that? Sure! But I think that if you look for names with Ed in it, that's a good place to start too. Edmund is my favorite Ed- name. Others: Edison, Edgar, Edwin. Actually, I really like Edison too!
People use it as a nn for Frederick.
Or for Thaddeus. Bit of a stretch, but so what? :)