TD permits study, including full-time enrolment, so a change to a student status is not required for that purpose alone. It does not authorize employment of any kind, and it does not affect whether a school admits the applicant or how tuition is assessed.
Know what the status is answering
TD answers one question: whether studying is permitted while the principal holds TN status. It says nothing about admission standards, program prerequisites, or the rate a school charges. Families sometimes discover late that the immigration side was never the obstacle. Confirm the academic and financial requirements with the institution directly, in writing, while the immigration steps proceed on their own track.
TN still requires citizenship of Canada or Mexico, a qualifying listed profession with its specific credential requirements, prearranged professional employment, and temporary entry. Confirm first that the degree, diploma or licence corresponds to the profession being claimed and to the duties described in the offer, since that analysis is unchanged by a name change. The applicant and employer should check the responsible state board's requirements for sealing drawings or taking responsible charge of designs, including any examination, experience or comity rules.
Ask the employer to identify the tasks assigned to the applicant, including any mixed responsibilities.