Step 1: To name a transplant, ask how closely the donor and recipient match genetically.
Step 2: Mother and son share species but not an identical genome, and a transfer between two non-identical members of the same species is by definition an allograft, the commonest form of human organ transplant.
Step 3: Since their tissue types are not the same, immunosuppression is required afterwards to prevent rejection of the donated kidney.
Step 4: It is not an isograft (that needs identical twins), not an autograft (own tissue), and not a xenograft (across species).
\[\boxed{\text{Allograft}}\]