Can you include the same customer in both the training and test sets? Is it reasonable to include the same customer in both train and test samples?
I'm working in panel data logistic regression.  I'm actually trying to calculate a probability of default for each customer, so logit model is used to predict the pd of customers, I couldn't be so sure whether I need to include the same customer in both train and test sample. 
 A: While testing, what you want to know is whether your model can generalize well to unseen data. Having samples already seen by your model during training does not help this cause.
Ideally you do not want the same sample to be present in both test and train data as this leads to optimistic results during testing.
A: You mean each customer has multiple samples right?
I faced the same problem when trying to perform image classification on MRIs. Do you just to the regular train/test split? But this would cause images of the same subject be both in the training and test sets. Instead we chose to make the split based on the subjects and not the images. Our reckoning was that the network might learn characteristics about the shape of the head of each subject (i.e. people either healthy or sick) during training and use them for testing. This way it would actually cheat during testing because it's not diagnosing disease but remembering the shape of the scull. By splitting based on subjects, way we made sure that the network can't cheat in that way because it hasn't seen seen any other frames of the same person.
Now on to your case. If your data contains any features about each customer (e.g. demographic features), I think the safest is to split the customers not the samples.
