Final answer:
Perry Parks is assigned a unique patient number at the hospital using an alphanumeric numbering system, which combines letters and numbers to ensure patient confidentiality and reduce errors.
Step-by-step explanation:
The type of numbering system being used to assign Perry Parks a patient number based on the letters of his name and his date of birth is known as an alphabetic-numeric or alphanumeric numbering system. This system combines both alphabetic characters and numerical digits to create a unique identifier for patients. This is particularly useful in medical record-keeping as it helps in preventing duplications and errors, and enhances privacy by not revealing personal information outright.