Yes, he certainly looks Havanese shape! Where did you get him? Did he come from a good breeder? If so, you should be asking the breeder about his coat. If he came from a pet store (and therefore is a puppy mill dog) or from a back yard breeder, he COULD have some sort of illness, and need to see the vet, or he COULD be healthy, but just be poorly bred and have a bad coat.
I wouldn't doubt that he's a Havanese, but I'd do things in this order:
1. Take him to the vet to rule out illness
2. Talk to the breeder if possible
3. Talk to a good canine nutritionist, to make sure he's on the healthiest diet possible
If he's ill in some way, you need to make a decision whether you want to (and can afford to) treat it. If not, you need to see about returning him. If you can afford to treat him, I will assume you want to keep him anyway. If he comes from a good breeder, they still might be willing to help you. If he comes from a pet store, you might be able to force their hand a bit, by going after them for selling you an ill puppy. Maybe they will give you a partial refund to help toward medical expenses. If he came from a BYB... good luck.
If you find that he's healthy, but just has a funky coat, enjoy him anyway! He's a cute little guy, and I bet he's sweet too! You saw some photos of Suzi's dog, Maddie. She went through a stage of looking pretty moth eaten, and she's adorable now, as a grown-up. She doesn't have a gorgeous "show coat", but she's cute just the way she is, and requires less grooming than a lot of the ones with a ton of coat.
We've seen other puppies on the forum like Maddie too... whose coat was pretty thin as a puppy, but looked much better as adults. It could be that your little guy is like them!