I have a donated organ, will I be more susceptible to encephalitis infection?

Immuno. Transplant recipients can be more susceptible to infections given the anti rejection meds can suppress the normal immune function.
If immunosuppressed. Encephalitis, inflammation of the brain, can be caused by viruses, bacteria, fungi, parasites, unknown causes, etc... Herpes types 1 & 2, epstein barr virus, varicella (chicken pox, shingles) virus, polio virus, coxsackie (hand-foot-mouth) virus, or mosquito-borne viruses can sometimes cause encephalitis. A suppressed immune system makes one more likely to get these diseases and get encephalitis.