I live in deep South Texas just north of the Mexican border, so I am fairly well versed in cooking many kinds of Tex-Mex meals. But once in a while, I like to 'tweak' recipes and make something different for the sake of variety. I have also heard these enchiladas called "Yankee Enchiladas". I categorized this dish as "American" cuisine, as it is not really considered a Mexican style dish. They don't make it this way in Mexico.
Preheat oven to 375 degrees. Open cans of cream of chicken soup and green enchilada sauce and mix together until smooth. Open can of canned chicken breast chunks and empty the liquid only into the sauce mixture and stir in.
Soften tortillas in the microwave for a few seconds to make them more pliable. With your hands, pull apart and shred the canned chicken chunks and place a small amount (about an ounce) in each of the tortillas. Spoon in about 1-2 Tbsps of the sauce on top of the chicken and then spread a little of the shredded cheese inside each enchilada. Roll up as tightly as possible.
Arrange the enchiladas not too tightly in the bottom of a 10" X 10" baking dish or similar size, sprayed first with non-stick spray. Pour sauce over all, making sure sauce gets in between and all around the enchiladas. Sprinkle diced onion over all and then cover with the rest of the shredded cheese.
Bake uncovered in 375 degree oven for about 45 to 55 minutes. The cheese on top should be a little brown and bubbly. Let sit on top of the stove for about 10 minutes, then serve hot. Best to use a wide spatula so they don't fall apart when serving.
Recommend serving with hot Tex-Mex style refried beans and Mexican rice. You can garnish with a handful of diced green onion tops (optional). You can also serve with sliced black olives and with a dollop of sour cream.
SIDE NOTE: If you prefer to do this, instead of using green enchilada sauce, buy a can of crushed tomatillos and add 3 or 4 tablespoons of your favorite salsa to it for flavor. You could also add a small can of mild diced green chilies if you want a little extra 'spice'. Then combine with your Cream of Chicken soup. I have done it either way and both are very good.