If we decide that we are both going to have artificial insemination, can we use sperm from the same donor?

Generally, each insemination would use a different sperm donor. Sperm donation in many countries is anonymous and the donor is assigned by the ferrtility clinic based on the immunological and physical characteristics of the patient.

However, if both women can be matched with the same donor based on these criteria, and there is sufficient sample available, theoretically it is possible, if not probable.

If in a state or country that allows free selection of the sperm donor, then yes, it is possible to use sperm from the same donor.