Explain the actual relationship and obtain accurate confirmation rather than silently replacing one name with another.
Preserve the reason for the difference
Identify which company employs, pays and proposes to fund the principal. A difference may need clarification without necessarily being an error or a prohibited arrangement. Use the current official case requirements and preserve genuine records; a new cover letter cannot change the underlying corporate facts.
Identity and family information, a precise description of the actual proposal, and specific questions about eligibility and funding, followed by whatever USCIS forms and evidence the official instructions require after the initial step. The vetting file is personal: passports, civil records for the marriage and the children, addresses and travel history, and a frank account of anything in a person's background that might bear on admissibility, disclosed to an attorney early rather than discovered later. Alongside the funds narrative, expect the ordinary civil record to be requested: birth, marriage and any divorce or death certificates, police records from countries of long residence, and identity documents in every name the applicant has used. If a government notice later states a birth place or classification you believe is wrong, investigate the conflict and respond through the official channel rather than repeating information you know to be inaccurate.