Soft stools in puppies is not a normal finding, but it is certainly a common problem. Times of stress, such as transition to a new home, can make the susceptible to some infections.... coccidia is the most common, but giardia or clostridia overgrowth are also possible. They typically cause soft stools, sometimes even with a bit of blood, but generally no vomit and the puppies are eating well and otherwise acting normal.
There are more serious problems that can cause soft stool such as parvo virus infection, but that cause vomiting, weakness, and signs of illness.
The canned pumpkin can help firm up the stool, but if this is something like coccidia then it should be treated sooner than later. I would try to take him to a veterinarian in the next day or so to get a fecal test done so they can choose the right medication to give him. If he is ill (vomiting, lethargic, not eating) then he should go even sooner.
I hope that helps, but if you have additional questions please let me know. If not, please rate my answer.