If you get an Italian Greyhound puppy from a breeder, they would give you a feeding schedule and it's important to stick to the same routine, feeding the same puppy food to avoid any tummy upsets.
You can change a puppy's diet, but this needs to be done very gradually always making sure they don't develop any digestive upsets and if they do, it's best to put them back on their original diet and to discuss things with the vet before attempting to change it again. It's also important that puppies be fed frequently throughout the day because they are susceptible to developing hypoglycemia.
Older dogs are not known to be fussy or finicky eaters, but this does not mean you can feed them a lower quality diet. It's best to feed a mature dog twice a day, once in the morning and then again in the evening, making sure it's good quality food that meets all their nutritional requirements.
It's also important that dogs be given the right amount of exercise so they burn off any excess calories or they might gain too much weight which can lead to all sorts of health issues. Obesity can shorten a dog's life by several years so it's important to keep an eye on their waistline from the word go.