A chili dog is just not a chili dog without raw onions. Do you prefer the onions chopped or grated? Sometimes I just like to chop up the onions to give the dogs an onion flavor and sometime I like to grate them really fine and mix the grated onions with the chili.
The way to use onions most effectively in hamburgers is to mix the ground meat with chopped onions. It's the way my mother did it, and it's the way I do it.