Baby Doc?

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My boss named her son David Oliver C****. They chose that name because David honors a family member, and Oliver was a name they liked. They have no intentions of calling him David. They want him to go solely by Doc (his initials). (He is a Physical Therapist and she is a Pharmacist, so Doc is fitting for their family). She is just curious what you would think if you were introduced to a baby called "Doc," and whether it would be acceptable for him to go by this nickname in school. They really do not care for the name David by itself.