The extension request must be verified by someone properly authorized to sign on behalf of the applicant. See 37 C.F.R. §2.193(e)(1) and TMEP §611.03(a) regarding persons properly authorized to sign on behalf of the applicant. If the extension request is unsigned or signed by the wrong party, a properly signed substitute verification must be submitted before the expiration of the deadline for filing the statement of use. 37 C.F.R. §§2.89(a)(3), 2.89(b)(3). Generally, the USPTO will not question the authority of the person who signs a verification unless there is an inconsistency in the record as to the signatory’s authority to sign.
If the extension request is not filed within one year after it is signed, the USPTO may require a substitute verification or declaration under 37 C.F.R. §2.20 that the applicant has a continued bona fide intention to use the mark in commerce, for a trademark or service mark, or that the applicant has a continued bona fide intention, and is entitled, to exercise legitimate control over the use of the mark in commerce, for a collective or certification mark. 37 C.F.R. §2.89(h); see TMEP §804.03.
See TMEP §611 regarding signature on correspondence filed with the USPTO.