Not necessarily, but the employer and actual arrangement must be explained accurately. A name difference is a question to resolve, not a fact to omit.
Identify the entity responsible for the offer
Ask whether the names refer to a trading style, affiliate or different employer, and obtain reliable confirmation. The proposed work still must fit a listed profession with the required qualifications and citizenship. Do not treat a payroll processor or a recognizable brand as proof of the employment relationship without understanding its role.
The practical fix costs nothing: ask the employer for a letter that states the position is an engineering role, describes engineering duties in concrete terms, and notes the internal administrative title separately if payroll requires it. Before filing, the actual duties on the turnaround, not the internal job title, should be checked against the engineer entry's definition, because a technologist doing engineer-labeled work does not become an engineer for TN purposes simply because payroll calls the position that. Where the answer is neither Canadian nor Mexican, this route is unavailable regardless of the credentials, the offer, or the years spent living in Canada, and continuing to plan around it wastes the applicant's money and the employer's patience.