FAA Order 8080.6H - Conduct of Airman Knowledge Tests states, on page 3-2, the following with respect to an "Underage Applicant" (under age 18):
Underage Applicant. For an applicant under the age of 18, a parent or legal guardian may
have to accompany the applicant and, after identifying themselves as described above, may attest
to the applicant’s identity. (Refer to FAA Order 8900.1, Volume 5, Chapter 1, Section 3.) The
parent or legal guardian must present a valid and current form of identification as described in
subparagraph 1b above.
(emphasis is mine)
That a parent or legal guardian may
have to accompany the applicant is likely due to the fact that the applicant (under age 18) may not possess a required form of identification, such as that noted on page 3-1 in FAA Order 8080.6H (link above):
Acceptable Forms of Identification. The proof of applicant identification may be
presented in more than one form.
(1) Acceptable forms of photo identification for U.S. citizens and resident aliens include:
• Driver’s license issued by a U.S. state or territory,
• U.S. Government identification card,
• U.S. Military identification card, or
• Passport or alien residency card