Even if your new puppy is picture-perfect in every single way, occasional whining is pretty much inevitable. If he whines a lot and it's breaking your heart that you can't comfort him, consider all of the possible root causes of his vocalization, whether pure loneliness or the basic need to go to the bathroom.
If your pooch is in the midst of undergoing crate training for housebreaking purposes, then his whining could be a request -- or demand -- to be let out of the thing. Puppies are full of excess energy, and being inside of a crate doesn't exactly allow for too much fun sprinting and exploring. If you hear your puppy whining up a storm every time you come back home after an hour of errands, it probably means that he's ready to get out -- now.
Dogs often bond to people quickly, and separation anxiety is a possibility even if your puppy has only been in your life for a brief period of time. If you reside in an apartment complex and your downstairs neighbor can hear your puppy's whining and wailing all day while you're at work, then it's because your cutie has not learned yet how to cope with being on his own. Apart from whining, separation anxiety is often associated with a lot of other not-so-pleasant behaviors -- think nonstop barking, scratching home interiors, chewing and frenetic activity.
Whining in puppies sometimes is a helpful request to be allowed outdoors to eliminate, whether "No.1" or "No. 2." If your wee pooch still isn't adjusted to his bathroom schedule, then he might whine as a way of letting you know that he's uncomfortable and has to go -- stat. This is especially common right after puppies finish either eating or drinking water. Keep your eyes open for any other indications of the need to use the potty, such as scratching the front door or simply sitting in front of it.
Puppies learn fast, and if your little one has already learned that whining is a surefire way of getting your fast attention, then don't surprised if he does it over and over again -- yikes.
One of the most sweetly endearing things about puppies is their giddy and overwhelmed natures, but to an extent. If your puppy whines excessively every time he even sees you walking his way, he's happy to see you and just doesn't know what to do with all of the thrill.
Immoderate whining can also indicate that something is amiss in your puppy. Perhaps he has a belly ache. Perhaps he fell down somewhere and feels like he has a wound. If your puppy whines a lot and you have no idea why, never rule out the possibility of health ailments. Take your puppy to the veterinarian immediately if you have any reason to think that he's whining out of pain.